Abstract
Let Image be the affine Hecke algebra corresponding to the group GLl over a p-adic field with residue field of cardinality q. We will regard Image as an associative algebra over the field Image . Consider the Image -module W induced from the tensor product of the evaluation modules over the algebras Image and Image . The module W depends on two partitions ¿ of l and µ of m, and on two non-zero elements of the field Image . There is a canonical operator J acting on W; it corresponds to the trigonometric R-matrix. The algebra Image contains the finite dimensional Hecke algebra Hl+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 ¿.
| Original language | English |
|---|---|
| Pages (from-to) | 1345-1376 |
| Number of pages | 32 |
| Journal | European Journal of Combinatorics |
| Volume | 25 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Nov 2004 |
Keywords
- Algebra, Pure Mathematics