Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648358 | Discrete Mathematics | 2009 | 7 Pages |
Abstract
We compute a stable formula for the Hilbert series of the invariant algebra of polynomial functions on â¨i=1rCni under the action of U(n1)Ãâ¯ÃU(nr), when viewed as real vector space. This situation has a physical interpretation as it is the quantum analog of an r-particle classical system in which the ith particle has ni classical states. The stable formula involves only elementary combinatorics, while its derivation involves the representation theory of the symmetric group. In particular, the Kronecker coefficients play an important role.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Michael W. Hero, Jeb F. Willenbring,