Abstract
After establishing a geometric Schur–Weyl duality in a general setting, we recall this duality in type A in the finite and affine case. We extend the duality in the affine case to positive parts of the affine algebras. The positive parts have nice ideals coming from geometry, allowing duality for quotients. Some of the quotients of the positive affine Hecke algebra are then identified to some cyclotomic Hecke algebras and the geometric setting allows the construction of canonical bases.
Original language | English |
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Pages (from-to) | 230–247 |
Number of pages | 17 |
Journal | Journal of Algebra |
Volume | 321 |
Issue number | 1 |
Early online date | 16 Dec 2008 |
DOIs | |
Publication status | Published - Jan 2009 |
Keywords / Materials (for Non-textual outputs)
- REPRESENTATION-THEORY
- quantum groups
- Affine Hecke algebra
- Schur–Weyl duality