Kostant's generating functions and McKay-Slodowy correspondence

Abstract

Let $N⊴G$ be a pair of finite subgroups of ${\mathrm{SL}}_2(\mathbb{C})$ and $V$ a finite-dimensional fundamental $G$-module. We study Kostant's generating functions for the decomposition of the ${\mathrm{SL}}_2(\mathbb{C})$-module $S^k(V)$ restricted to $N⊲G$ in connection with the McKay-Slodowy correspondence. In particular, the classical Kostant formula was generalized to a uniform version of the Poincaré series for the symmetric invariants in which the multiplicities of any individual module in the symmetric algebra are completely determined.

arXiv comment15 pages

References in corpus (4)

• Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations
• The Coxeter element and the branching law for the finite subgroups of SU(2)
• Poincaré series, exponents of affine Lie algebras, and McKay-Slodowy correspondence
• Poincaré series of relative symmetric invariants for SL${}_n(\mathbb{C})$