Lusztig q-weight multiplicities and their generalizations
| 구분 | 박사학위 논문 발표 |
|---|---|
| 일정 | 2026-06-05(금) 12:30~16:00 |
| 세미나실 | 129동 309호 |
| 강연자 | 최현재 |
| 담당교수 | 이승진 |
| 기타 |
Lusztig q-weight multiplicities extend the Kostka-Foulkes polynomials to a broader range of Lie types. In this talk, we investigate these multiplicities through the framework of Kirillov--Reshetikhin crystals. For type C with dominant weights and type B with dominant spin weights, we give combinatorial formulas for Lusztig's q-weight multiplicities in terms of energy functions on Kirillov--Reshetikhin crystals. These formulas generalize the charge formula for Kostka-Foulkes polynomials in type A.
We also introduce level-restricted q-weight multiplicities for nonexceptional types and prove their positivity by giving combinatorial formulas. We conclude with two further generalizations, namely a type C Catalan-Kostka generalization using root ideals and a noncommutative generalization using noncommutative Kostka polynomials and immaculate tableaux.