Jonah Blasiak - A canonical basis for Garsia-Procesi modules

dmtcs:2858 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2858
A canonical basis for Garsia-Procesi modulesConference paper

Authors: Jonah Blasiak 1

  • 1 Department of Computer Science, University of Chicago

We identify a subalgebra ˆH+n of the extended affine Hecke algebra ˆHn of type A. The subalgebra ˆH+n is a u-analogue of the monoid algebra of Sn0n and inherits a canonical basis from that of ˆHn. We show that its left cells are naturally labeled by tableaux filled with positive integer entries having distinct residues mod n, which we term positive affine tableaux (PAT). We then exhibit a cellular subquotient Rn1 of ˆH+n that is a u-analogue of the ring of coinvariants [y1,,yn]/(e1,,en) with left cells labeled by PAT that are essentially standard Young tableaux with cocharge labels. Multiplying canonical basis elements by a certain element πˆH+n corresponds to rotations of words, and on cells corresponds to cocyclage. We further show that Rn1 has cellular quotients Rλ that are u-analogues of the Garsia-Procesi modules Rλ with left cells labeled by (a PAT version of) the λ -catabolizable tableaux.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Garsia-Procesi modules,affine Hecke algebra,canonical basis,symmetric group,k-atoms,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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