A mixed hook-length formula for affine Hecke algebras
| dc.creator | Nazarov, Maxim | |
| dc.date | 2003-07-08 | |
| dc.date | 2004-04-05 | |
| dc.date.accessioned | 2026-07-07T04:59:28Z | |
| dc.date.available | 2026-07-07T04:59:28Z | |
| dc.description | Consider the affine Hecke algebra $H_l$ corresponding to the group $GL_l$ over a $p$-adic field with the residue field of cardinality $q$. Regard $H_l$ as an associative algebra over the field $C(q)$. 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 non-zero elements of the field $C(q)$. There is a canonical operator $J$ acting on $W$, it corresponds to the trigonometric $R$-matrix. The algebra $H_{l+m}$ contains the finite dimensional Hecke algebra of rank $l+m$ as a subalgebra, and the operator $J$ commutes with the action of this subalgebra on $W$. 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 give a formula for the ratio of two eigenvalues of $J$, corresponding to the ``highest'' and the ``lowest'' components. As an application, we derive the well known $q$-analogue of the hook-length formula for the number of standard tableaux of shape $λ$. | |
| dc.description | 36 pages, final version | |
| dc.identifier | https://arxiv.org/abs/math/0307091 | |
| dc.identifier | http://arxiv.org/abs/math/0307091 | |
| dc.identifier | European J. Combinatorics 25 (2004), 1345-1376 | |
| dc.identifier | doi:10.1016/j.ejc.2003.10.010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67999 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.title | A mixed hook-length formula for affine Hecke algebras | |
| dc.type | text |