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Path combinatorics and light leaves for quiver Hecke algebras

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1 Published in 2021 at "Mathematische Zeitschrift"

DOI: 10.1007/s00209-021-02829-0

Abstract: We recast the classical notion of “standard tableaux" in an alcove-geometric setting and extend these classical ideas to all “reduced paths" in our geometry. This broader path-perspective is essential for implementing the higher categorical ideas… read more here.

Keywords: hecke algebras; path combinatorics; light leaves; combinatorics light ... See more keywords

Positive Jantzen sum formulas for cyclotomic Hecke algebras

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1 Published in 2022 at "Mathematische Zeitschrift"

DOI: 10.1007/s00209-021-02957-7

Abstract: This paper proves a “positive” Jantzen sum formula for the Specht modules of the cyclotomic Hecke algebras of type A and uses it to obtain new bounds on decomposition numbers. Quite remarkably, our results are proved… read more here.

Keywords: sum; jantzen sum; hecke algebras; sum formula ... See more keywords

Characters of Iwahori–Hecke algebras

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0 Published in 2017 at "Israel Journal of Mathematics"

DOI: 10.1007/s11856-018-1779-9

Abstract: In this paper we prove a quantum generalization of Regev’s theorems (Israel. J. Math. 195 (2013), 31–35) by applying the Schur–Weyl duality between the quantum superalgebra and Iwahori–Hecke algebra. We also present an alternative proof… read more here.

Keywords: hecke algebras; characters iwahori; iwahori hecke;

Affine Hecke Algebras via DAHA

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1 Published in 2017 at "Arnold Mathematical Journal"

DOI: 10.1007/s40598-018-0082-5

Abstract: A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic… read more here.

Keywords: hecke algebras; affine hecke; via daha; algebras via ... See more keywords

Cyclotomic Yokonuma–Hecke algebras are cyclotomic quiver Hecke algebras

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0 Published in 2017 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2017.03.004

Abstract: We prove that cyclotomic Yokonuma–Hecke algebras of type A are cyclotomic quiver Hecke algebras and we give an explicit isomorphism with its inverse, using a similar result of Brundan and Kleshchev on cyclotomic Hecke algebras.… read more here.

Keywords: hecke algebras; algebras cyclotomic; hecke; cyclotomic quiver ... See more keywords

Parabolic inductions for pro-p-Iwahori Hecke algebras

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0 Published in 2019 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2019.106776

Abstract: We give some properties of parabolic inductions and their adjoint functors for pro-$p$-Iwahori Hecke algebras. read more here.

Keywords: hecke algebras; iwahori hecke; inductions pro; parabolic inductions ... See more keywords

A categorification of Hecke algebras with parameters 1 and v

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1 Published in 2019 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2019.06.031

Abstract: We categorify the Hecke algebra with parameters 1 and v using a variation of the category of Soergel bimodules. read more here.

Keywords: hecke algebras; hecke; categorification hecke; algebras parameters ... See more keywords

On the center of quiver Hecke algebras

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1 Published in 2017 at "Duke Mathematical Journal"

DOI: 10.1215/00127094-3792705

Abstract: We compute the equivariant cohomology ring of the moduli space of framed instantons over the affine plane. It is a Rees algebra associated with the center of cyclotomic degenerate affine Hecke algebras of type A.… read more here.

Keywords: hecke algebras; quiver hecke; center; center quiver ... See more keywords

Hecke * * -algebras on locally compact hypergroups

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0 Published in 2020 at "Georgian Mathematical Journal"

DOI: 10.1515/gmj-2020-2078

Abstract: Abstract In this paper, for a discrete hypergroup K and its subhypergroup H, we initiate the related Hecke * {*} -algebra which is an extension of the classical one, and study its basic properties. Especially,… read more here.

Keywords: hecke algebras; algebras locally; compact hypergroups; locally compact ... See more keywords