1Dept. of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A. 2Dept. of Mathematics, University of Wisconsin, Eau Claire, WI 54701-4004, U.S.A.
Journal of Lie Theory, Tome 19 (2009) no. 4, pp. 771-795
\def\C{{\Bbb C}} \def\R{{\Bbb R}} \def\HH{{\Bbb H}} This work concerns linear multiplicity free actions of the complex groups $G_\C=GL(n,\C)$, $GL(n,\C)\times GL(n,\C)$ and $GL(2n,\C)$ on the vector spaces $V=Sym(n,\C)$, $M_n(\C)$ and $Skew(2n,\C)$. We relate the canonical invariants in $\C[V \oplus V^*]$ to spherical functions for Riemannian symmetric pairs $(G,K)$ where $G=GL(n,\R)$, $GL(n,\C)$ or $GL(n,\HH)$ respectively. These in turn can be expressed using three families of classical zonal polynomials. We use this fact to derive a combinatorial algorithm for the generalized binomial coefficients in each case. Many of these results were obtained previously by Knop and Sahi using different methods.
Chal Benson
1
;
R. Michael Howe
2
;
Gail Ratcliff
1
1
Dept. of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A.
2
Dept. of Mathematics, University of Wisconsin, Eau Claire, WI 54701-4004, U.S.A.
Chal Benson; R. Michael Howe; Gail Ratcliff. Invariant Polynomials for Multiplicity Free Actions. Journal of Lie Theory, Tome 19 (2009) no. 4, pp. 771-795. http://geodesic.mathdoc.fr/item/JOLT_2009_19_4_a8/
@article{JOLT_2009_19_4_a8,
author = {Chal Benson and R. Michael Howe and Gail Ratcliff},
title = {Invariant {Polynomials} for {Multiplicity} {Free} {Actions}},
journal = {Journal of Lie Theory},
pages = {771--795},
year = {2009},
volume = {19},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2009_19_4_a8/}
}
TY - JOUR
AU - Chal Benson
AU - R. Michael Howe
AU - Gail Ratcliff
TI - Invariant Polynomials for Multiplicity Free Actions
JO - Journal of Lie Theory
PY - 2009
SP - 771
EP - 795
VL - 19
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2009_19_4_a8/
ID - JOLT_2009_19_4_a8
ER -
%0 Journal Article
%A Chal Benson
%A R. Michael Howe
%A Gail Ratcliff
%T Invariant Polynomials for Multiplicity Free Actions
%J Journal of Lie Theory
%D 2009
%P 771-795
%V 19
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2009_19_4_a8/
%F JOLT_2009_19_4_a8
