Hecke Algebra Actions on the Coinvariant Algebra

Adin, Ron M.; Postnikov, Alexander; Roichman, Yuval

doi:10.1006/jabr.2000.8441

Cited by 10 publications

(10 citation statements)

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“…(2.9) Here we follow [1] and use a nonstandard presentation of the Hecke algebra so that our specialization at q = 0 agrees with the form of the 0-Hecke algebra defined above. The usual conventions replace T i with −T i .…”

Section: 13mentioning

confidence: 99%

Oddification of the Cohomology of Type A Springer Varieties

Lauda

Russell

2013

International Mathematics Research Notices

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We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are 'odd' analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top degree component of the odd cohomology of Springer varieties is identified with the corresponding Specht module of the Hecke algebra at q = −1.

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Section: 13mentioning

confidence: 99%

Oddification of the Cohomology of Type A Springer Varieties

Lauda

Russell

2013

International Mathematics Research Notices

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“…There is a well-known action of the Hecke algebra H n (q) on R n [2]; we prove that the same is true for R…”

Section: Resultsmentioning

confidence: 56%

“…is the classical coinvariant algebra R n of the symmetric group S n . There is a well-known action of the Hecke algebra H n (q) on R n [2]; we prove that the same is true for R n,k is therefore a graded H n (q)-module. The proof of Proposition 2.2 is a slightly tedious computation and will be postponed to Section 3.…”

Section: Resultsmentioning

confidence: 56%

“…For q generic (not zero or a root of unity), as it will be in this paper, the F -algebra H n (q) is semisimple and has irreducible representations indexed by partitions λ ⊢ n. Hecke algebras naturally arise and play significant roles in many places, such as automorphic forms, combinatorics, quantum groups, and the representation theory of symmetric groups and general linear groups [4]. Finding Hecke deformations of actions of the symmetric group is a pervasive theme in algebraic combinatorics (see, e.g., [2,3]).…”

Section: Introductionmentioning

confidence: 99%

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Hall-Littlewood polynomials and a Hecke action on ordered set partitions

Huang

Rhoades

Scrimshaw

2019

Proc. Amer. Math. Soc.

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“…This negated version yields, in most cases, more elegant q-analogues (see e.g. [1]). The author is very grateful to the anonymous referee for this suggestion.…”

Section: Introductionmentioning

confidence: 99%