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- W2950127346 abstract "This paper provides a combinatorial dictionary between three sets of objects: Bernstein-Zelevinsky multisegments, Kleshchev multipartitions, and the irreducible modules of the affine Hecke algebra $H_n$ (for generic $q$). In particular, we compute the action of the crystal operator $tilde{e}_i$ (a refinement of socle of Restriction) on an irreducible module both in terms of its parameterization by multisegments and by multipartitions. In other words, we give explicit crystal graph isomorphisms. A byproduct is the determination of which multisegments parameterize modules of the {it cyclotomic} Hecke algebra $H_n^lambda$. The theorems also explain why the rule for computing $tilde{e}_i$ mirrors the rule we know for that on a tensor product of crystal graphs. We also give a construction of the irreducible module parameterized by a multipartition without relying on a choice of path in the crystal graph. The proofs given here are elementary and do not rely on any geometry." @default.
- W2950127346 created "2019-06-27" @default.
- W2950127346 creator A5084585699 @default.
- W2950127346 date "2001-07-06" @default.
- W2950127346 modified "2023-09-27" @default.
- W2950127346 title "Parameterizing Hecke algebra modules: Bernstein-Zelevinsky multisegments, Kleshchev multipartitions, and crystal graphs" @default.
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