Mixed hook-length formula for degenerate affine Hecke algebras
| dc.creator | Nazarov, Maxim | |
| dc.date | 1999-06-22 | |
| dc.date | 2003-07-08 | |
| dc.date.accessioned | 2026-07-07T06:33:01Z | |
| dc.date.available | 2026-07-07T06:33:01Z | |
| dc.description | Take the degenerate affine Hecke algebra $H_{l+m}$ corresponding to the group $GL_{l+m}$ over a $p$-adic field. Consider the $H_{l+m}$-module $W$ induced from the tensor product of the evaluation modules over the algebras $H_l$ and $H_m$. The module $W$ depends on two partitions $λ$ of $l$ and $μ$ of $m$, and on two complex numbers $z$ and $w$. There is a canonical operator $J$ acting in $W$, it corresponds to the rational Yang $R$-matrix. The algebra $H_{l+m}$ contains the symmetric group $S_{l+m}$, and $J$ commutes with the action of $S_{l+m}$ in $W$. Under this action, $W$ decomposes into irreducible subspaces according to the Littlewood-Richardson rule. We compute the eigenvalues of $J$, corresponding to certain multiplicity-free irreducible components of $W$. In particular, we obtain a nice formula for the ratio of two eigenvalues of $J$, corresponding to the "highest" and "lowest" (multiplicity-free) irreducible components of $W$. | |
| dc.description | AmS-TeX, 12 pages, final version | |
| dc.identifier | https://arxiv.org/abs/math/9906148 | |
| dc.identifier | http://arxiv.org/abs/math/9906148 | |
| dc.identifier | Lecture Notes in Math. 1815 (2003), 223-236 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99055 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.title | Mixed hook-length formula for degenerate affine Hecke algebras | |
| dc.type | text |