Lusztig's q-analogue of weight multiplicity and one-dimensional sums for affine root systems
| dc.creator | Lecouvey, Cedric | |
| dc.creator | Shimozono, Mark | |
| dc.date | 2005-08-25 | |
| dc.date | 2008-10-15 | |
| dc.date.accessioned | 2026-07-07T10:10:02Z | |
| dc.date.available | 2026-07-07T10:10:02Z | |
| dc.description | In this paper we complete the proof of the X=K conjecture, that for every family of nonexceptional affine algebras, the graded multiplicities of tensor products of symmetric power Kirillov-Reshetikhin modules known as one-dimensional sums, have a large rank stable limit X that has a simple expression (called the K-polynomial) as nonnegative integer combination of Kostka-Foulkes polynomials. We consider a subfamily of Lusztig's q-analogues of weight multiplicity which we call stable KL polynomials and denote by KL. We give a type-independent proof that K=KL. This proves that X=KL: the family of stable one-dimensional sums coincides with family of stable KL polynomials. Our result generalizes the theorem of Nakayashiki and Yamada which establishes the above equality in the case of one-dimensional sums of affine type A and the Lusztig q-analogue of type A, where both are Kostka-Foulkes polynomials. | |
| dc.description | 28 pages; incorrect section 3.4 replaced | |
| dc.identifier | https://arxiv.org/abs/math/0508511 | |
| dc.identifier | http://arxiv.org/abs/math/0508511 | |
| dc.identifier | Adv. Math. 208 (2007) 438-466 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171504 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 17B37; 05E15; 81R10 | |
| dc.title | Lusztig's q-analogue of weight multiplicity and one-dimensional sums for affine root systems | |
| dc.type | text |