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- W4298912830 abstract "We identify a subalgebra pH_n of the extended affine Hecke algebra eH_n of type A. The subalgebra pH_n is a u-analogue of the monoid algebra of S_n ltimes ZZ_{geq 0}^n and inherits a canonical basis from that of eH_n. We show that its left cells are naturally labeled by tableaux filled with positive integer entries having distinct residues mod n, which we term emph{positive affine tableaux} (PAT). We then exhibit a cellular subquotient R_{1^n} of pH_n that is a u-analogue of the ring of coinvariants CC[y_1,...,y_n]/(e_1,...,e_n) with left cells labeled by PAT that are essentially standard Young tableaux with cocharge labels. Multiplying canonical basis elements by a certain element pi in pH_n corresponds to rotations of words, and on cells corresponds to cocyclage. We further show that R_{1^n} has cellular quotients R_lambda that are u-analogues of the Garsia-Procesi modules R_lambda with left cells labeled by (a PAT version of) the lambda-catabolizable tableaux. We give a conjectural description of a cellular filtration of pH_n, the subquotients of which are isomorphic to dual versions of R_lambda under the perfect pairing on R_{1^n}. We conjecture how this filtration relates to the combinatorics of the cells of eH_n worked out by Shi, Lusztig, and Xi. We also conjecture that the k-atoms of Lascoux, Lapointe, and Morse and the R-catabolizable tableaux of Shimozono and Weyman have cellular counterparts in pH_n. We extend the idea of atom copies of Lascoux, Lapoint, and Morse to positive affine tableaux and give descriptions, mostly conjectural, of some of these copies in terms of catabolizability." @default.
- W4298912830 created "2022-10-02" @default.
- W4298912830 creator A5064317285 @default.
- W4298912830 date "2010-01-10" @default.
- W4298912830 modified "2023-09-23" @default.
- W4298912830 title "Cyclage, catabolism, and the affine Hecke algebra" @default.
- W4298912830 doi "https://doi.org/10.48550/arxiv.1001.1569" @default.
- W4298912830 hasPublicationYear "2010" @default.
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