Generalized nil-coxeter algebras

Khare, A (2018) Generalized nil-coxeter algebras. In: 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018, 16-20 July 2018, Dartmouth CollegeHanover; United States.

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Abstract

Motivated by work of Coxeter (1957), we study a class of algebras associated to Coxeter groups, which we term 'generalized nil-Coxeter algebras'. We construct the first finite-dimensional examples other than usual nil-Coxeter algebras; these form a 2-parameter type A family that we term NCA(n, d). We explore the combinatorial properties of these algebras, including the Coxeter word basis, length function, maximal words, and their connection to Khovanov's categorification of the Weyl algebra. Our broader motivation arises from complex reflection groups and the Broué-Malle-Rouquier freeness conjecture (1998). With generic Hecke algebras over real and complex groups in mind, we show that the first 'non-usual' finite-dimensional examples NCA(n, d) are in fact the only ones, outside of the usual nil-Coxeter algebras. The proofs use a diagrammatic calculus akin to crystal theory. © FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

Item Type:	Conference Paper
Publication:	FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics
Publisher:	Formal Power Series and Algebraic Combinatorics
Additional Information:	cited By 0; Conference of 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 ; Conference Date: 16 July 2018 Through 20 July 2018; Conference Code:161385
Keywords:	Algebra; Calculations, Categorification; Combinatorial properties; Complex reflection groups; Coxeter groups; Diagrammatic calculus; Finite dimensional; Hecke algebras; Length functions, Combinatorial mathematics
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	07 Oct 2020 11:00
Last Modified:	07 Oct 2020 11:00
URI:	http://eprints.iisc.ac.in/id/eprint/66398

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