From 2bbbdba0f923d3cfdfe40bbb1933baf55daebbb1 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Mon, 10 Apr 2017 18:28:25 0400
Subject: [PATCH] books/bookvolbib RepresentationPackage1 references
MIMEVersion: 1.0
ContentType: text/plain; charset=UTF8
ContentTransferEncoding: 8bit
Goal: Axiom Maintenance
\index{Gollan, H.}
\index{Grabmeier, Johannes}
\begin{chunk}{axiom.bib}
@article{Goll90,
author = "Gollan, H. and Grabmeier, J.",
title = "Algorithms in Representation Theory and their
Realization in the Computer Algebra System Scratchpad",
journal = "Bayreuther Mathematische Schriften",
volume = "33",
year = "1990",
pages = "123",
algebra = "\newline\refto{package REP1 RepresentationPackage1}",
}
\end{chunk}
\index{Grabmeier, Johannes}
\index{Kerber, Adalbert}
\begin{chunk}{axiom.bib}
@article{Grab87,
author = "Grabmeier, Johannes and Kerber, Adalbert",
title = "The Evaluation of Irreducible Polynomial
Representations of the General Linear Groups
and of the Unitary Groups over Fields of
Characteristic 0",
journal = "Acta Applicandae Mathematica",
volume = "8",
year = "1987",
pages = "271291",
algebra = "\newline\refto{package REP1 RepresentationPackage1}",
abstract =
"We describe an efficient method for the computer evaluation of the
ordinary irreducible polynomial representations of general linear
groups using an integral form of the ordinary irreducible
representations of symmetric groups. In order to do this, we first
give an algebraic explanation of D. E. Littlewood's modification of
I. Schur's construction. Then we derive a formula for the entries of
the representing matrices which is much more concise and adapted to
the effective use of computer calculations. Finally, we describe how
one obtains — using this time an orthogonal form of the ordinary
irreducible representations of symmetric groups — a version which
yields a unitary representation when it is restricted to the unitary
subgroup. In this way we adapt D. B. Hunter's results which heavily
rely on Littlewood's methods, and boson polynomials come into the play
so that we also meet the needs of applications to physics.",
keywords = "axiomref"
}
\end{chunk}
\index{James, G.}
\index{Kerber, A.}
\begin{chunk}{axiom.bib}
@article{Jame81,
author = "James, G. and Kerber, A.",
title = "The Representation Theory of the Symmetric Group",
journal = "Encycl. of Math. and its Appl.",
volume = "16",
algebra = "\newline\refto{package REP1 RepresentationPackage1}",
publisher = "Cambr. Univ. Press",
year = "1981"
}
\end{chunk}

books/bookvol10.4.pamphlet  45 +++++++++++++++++
books/bookvolbib.pamphlet  82 ++++++++++++++++++++++++++++++++
changelog  3 +
patch  68 ++++++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
5 files changed, 173 insertions(+), 27 deletions()
diff git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet
index 499d057..b3e035f 100644
 a/books/bookvol10.4.pamphlet
+++ b/books/bookvol10.4.pamphlet
@@ 230687,7 +230687,7 @@ RepeatedSquaring(S) : SIG == CODE where
)set message auto off
)clear all
S 1 of 1
+S 1 of 3
)show RepresentationPackage1
R
R RepresentationPackage1(R: Ring) is a package constructor
@@ 230712,6 +230712,22 @@ RepeatedSquaring(S) : SIG == CODE where
R
E 1
+S 2 of 3
+t1:=matrix [[a,b,c],[d,e,f]]
+R
+R +a b c+
+R (1)  
+R +d e f+
+R Type: Matrix(Polynomial(Integer))
+E 2
+
+S 3 of 3
+antisymmetricTensors(t1,2)
+R
+R (2) [a e  b d a f  c d b f  c e]
+R Type: Matrix(Polynomial(Integer))
+E 3
+
)spool
)lisp (bye)
\end{chunk}
@@ 230731,6 +230747,16 @@ Note that instead of having parameters from Permutation this package
allows list notation of permutations as well: for example, [1,4,3,2]
denotes permutes 2 and 4 and fixes 1 and 3.
+t1:=matrix [[a,b,c],[d,e,f]]
+
+ +a b c+
+  
+ +d e f+
+
+antisymmetricTensors(t1,2)
+
+ [a e  b d a f  c d b f  c e]
+
See Also:
o )show RepresentationPackage1
@@ 230747,21 +230773,17 @@ o )show RepresentationPackage1
\cross{REP1}{tensorProduct} &
\end{tabular}
+See James\cite{Jame81}, Grabmeier\cite{Grab87},, Gollan\cite{Goll90}
+\label{package REP1 RepresentationPackage1}
\begin{chunk}{package REP1 RepresentationPackage1}
)abbrev package REP1 RepresentationPackage1
++ Authors: Holger Gollan, Johannes Grabmeier, Thorsten Werther
++ Date Created: 12 September 1987
++ Date Last Updated: 24 May 1991
++ References:
++ G. James, A. Kerber: The Representation Theory of the Symmetric
++ Group. Encycl. of Math. and its Appl. Vol 16., Cambr. Univ Press 1981;
++ J. Grabmeier, A. Kerber: The Evaluation of Irreducible
++ Polynomial Representations of the General Linear Groups
++ and of the Unitary Groups over Fields of Characteristic 0,
++ Acta Appl. Math. 8 (1987), 271291;
++ H. Gollan, J. Grabmeier: Algorithms in Representation Theory and
++ their Realization in the Computer Algebra System Scratchpad,
++ Bayreuther Mathematische Schriften, Heft 33, 1990, 123
+++ Jame81 The Representation Theory of the Symmetric Group
+++ Grab87 The Evaluation of Irreducible Polynomial Representations
+++ Goll90 Algorithms in Representation Theory
++ Description:
++ RepresentationPackage1 provides functions for representation theory
++ for finite groups and algebras.
@@ 230803,6 +230825,9 @@ RepresentationPackage1(R) : SIG == CODE where
++ representation with the sign representation of the symmetric group
++ Sn. The carrier spaces of the representation are the antisymmetric
++ tensors of the nfold tensor product.
+ ++
+ ++X t1:=matrix [[a,b,c],[d,e,f]]
+ ++X antisymmetricTensors(t1,2)
if R has commutative("*") then
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 3d3c827..187d77b 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 566,6 +566,23 @@ paragraph for those unfamiliar with the terms.
\end{chunk}
+\index{Gollan, H.}
+\index{Grabmeier, Johannes}
+\begin{chunk}{axiom.bib}
+@article{Goll90,
+ author = "Gollan, H. and Grabmeier, J.",
+ title = "Algorithms in Representation Theory and their
+ Realization in the Computer Algebra System Scratchpad",
+ journal = "Bayreuther Mathematische Schriften",
+ volume = "33",
+ year = "1990",
+ pages = "123",
+ algebra = "\newline\refto{package REP1 RepresentationPackage1}",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Gonshor, H.}
\index{AlgebraGivenByStructuralConstants}
\begin{chunk}{axiom.bib}
@@ 603,6 +620,55 @@ paragraph for those unfamiliar with the terms.
\end{chunk}
+\index{Grabmeier, Johannes}
+\index{Kerber, Adalbert}
+\begin{chunk}{axiom.bib}
+@article{Grab87,
+ author = "Grabmeier, Johannes and Kerber, Adalbert",
+ title = "The Evaluation of Irreducible Polynomial
+ Representations of the General Linear Groups
+ and of the Unitary Groups over Fields of
+ Characteristic 0",
+ journal = "Acta Applicandae Mathematica",
+ volume = "8",
+ year = "1987",
+ pages = "271291",
+ algebra = "\newline\refto{package REP1 RepresentationPackage1}",
+ abstract =
+ "We describe an efficient method for the computer evaluation of the
+ ordinary irreducible polynomial representations of general linear
+ groups using an integral form of the ordinary irreducible
+ representations of symmetric groups. In order to do this, we first
+ give an algebraic explanation of D. E. Littlewood's modification of
+ I. Schur's construction. Then we derive a formula for the entries of
+ the representing matrices which is much more concise and adapted to
+ the effective use of computer calculations. Finally, we describe how
+ one obtains — using this time an orthogonal form of the ordinary
+ irreducible representations of symmetric groups — a version which
+ yields a unitary representation when it is restricted to the unitary
+ subgroup. In this way we adapt D. B. Hunter's results which heavily
+ rely on Littlewood's methods, and boson polynomials come into the play
+ so that we also meet the needs of applications to physics.",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{James, G.}
+\index{Kerber, A.}
+\begin{chunk}{axiom.bib}
+@article{Jame81,
+ author = "James, G. and Kerber, A.",
+ title = "The Representation Theory of the Symmetric Group",
+ journal = "Encycl. of Math. and its Appl.",
+ volume = "16",
+ algebra = "\newline\refto{package REP1 RepresentationPackage1}",
+ publisher = "Cambr. Univ. Press",
+ year = "1981"
+}
+
+\end{chunk}
+
\index{AlgebraGivenByStructuralConstants}
\index{Reed, Mary Lynn}
\begin{chunk}{axiom.bib}
@@ 36940,22 +37006,6 @@ J. of Pure and Applied Algebra, 45, 225240 (1987)
\end{chunk}
\index{H. Gollan}
\index{Grabmeier, Johannes}
\begin{chunk}{axiom.bib}
@article{Goll90,
 author = "H. Gollan and Grabmeier, Johannes",
 title = "Algorithms in Representation Theory and their Realization
 in the Computer Algebra System Scratchpad",
 journal = "Bayreuther Mathematische Schriften",
 volume = "33",
 year = "1990",
 pages = "123",
 keywords = "axiomref"
}

\end{chunk}

\index{Grabmeier, Johannes}
\begin{chunk}{axiom.bib}
@misc{Grab91a,
diff git a/changelog b/changelog
index 87aef58..6f43e61 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,6 @@
+20170410 tpd src/axiomwebsite/patches.html 20170410.03.tpd.patch
+20170410 bmt books/bookvol10.4 RepresentationPackage1 references examples
+20170410 tpd books/bookvolbib RepresentationPackage1 references
20170410 bmt src/axiomwebsite/patches.html 20170410.02.bmt.patch
20170410 bmt books/bookvol10.4 antisymmetricTensors square matrix fix
20170410 bmt src/axiomwebsite/patches.html 20170410.01.bmt.patch
diff git a/patch b/patch
index 448a96a..d39eb7b 100644
 a/patch
+++ b/patch
@@ 1,4 +1,70 @@
books/bookvol10.4 antisymmetricTensors square matrix fix
+books/bookvolbib RepresentationPackage1 references
Goal: Axiom Maintenance
+\index{Gollan, H.}
+\index{Grabmeier, Johannes}
+\begin{chunk}{axiom.bib}
+@article{Goll90,
+ author = "Gollan, H. and Grabmeier, J.",
+ title = "Algorithms in Representation Theory and their
+ Realization in the Computer Algebra System Scratchpad",
+ journal = "Bayreuther Mathematische Schriften",
+ volume = "33",
+ year = "1990",
+ pages = "123",
+ algebra = "\newline\refto{package REP1 RepresentationPackage1}",
+}
+
+\end{chunk}
+
+\index{Grabmeier, Johannes}
+\index{Kerber, Adalbert}
+\begin{chunk}{axiom.bib}
+@article{Grab87,
+ author = "Grabmeier, Johannes and Kerber, Adalbert",
+ title = "The Evaluation of Irreducible Polynomial
+ Representations of the General Linear Groups
+ and of the Unitary Groups over Fields of
+ Characteristic 0",
+ journal = "Acta Applicandae Mathematica",
+ volume = "8",
+ year = "1987",
+ pages = "271291",
+ algebra = "\newline\refto{package REP1 RepresentationPackage1}",
+ abstract =
+ "We describe an efficient method for the computer evaluation of the
+ ordinary irreducible polynomial representations of general linear
+ groups using an integral form of the ordinary irreducible
+ representations of symmetric groups. In order to do this, we first
+ give an algebraic explanation of D. E. Littlewood's modification of
+ I. Schur's construction. Then we derive a formula for the entries of
+ the representing matrices which is much more concise and adapted to
+ the effective use of computer calculations. Finally, we describe how
+ one obtains — using this time an orthogonal form of the ordinary
+ irreducible representations of symmetric groups — a version which
+ yields a unitary representation when it is restricted to the unitary
+ subgroup. In this way we adapt D. B. Hunter's results which heavily
+ rely on Littlewood's methods, and boson polynomials come into the play
+ so that we also meet the needs of applications to physics.",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{James, G.}
+\index{Kerber, A.}
+\begin{chunk}{axiom.bib}
+@article{Jame81,
+ author = "James, G. and Kerber, A.",
+ title = "The Representation Theory of the Symmetric Group",
+ journal = "Encycl. of Math. and its Appl.",
+ volume = "16",
+ algebra = "\newline\refto{package REP1 RepresentationPackage1}",
+ publisher = "Cambr. Univ. Press",
+ year = "1981"
+}
+
+\end{chunk}
+
+
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 0616b81..7564263 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5692,6 +5692,8 @@ books/bookvol8.pamphlet strcpy > memmove in prt.c
books/bookvol8 fix memmove length calculation
20170410.02.bmt.patch
books/bookvol10.4 antisymmetricTensors square matrix fix
+20170410.03.tpd.patch
+books/bookvolbib RepresentationPackage1 references

1.7.5.4