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Factorial Q-functions and Tokuyama identities for classical Lie groups

Factorial Q-functions and Tokuyama identities for classical Lie groups
Factorial Q-functions and Tokuyama identities for classical Lie groups

Factorial characters of each of the classical Lie groups have recently been defined algebraically as rather simple deformations of irreducible characters. Each such factorial character has been shown to satisfy a flagged Jacobi–Trudi identity, thereby allowing for its combinatorial realisation in terms of first a non-intersecting lattice path model and then a tableau model. Here we propose algebraic definitions of factorial Q-functions of the classical Lie groups and translate these definitions into combinatorial realisations in terms of non-intersecting lattice path and primed shifted tableaux models. By way of some justification of our chosen definitions, it is then shown that our factorial Q-functions satisfy Tokuyama-type identities and relate some special case of these to other identities that have appeared in the literature.

0195-6698
89-113
Foley, Angèle M.
53e0c35d-e4bb-461d-9638-1d1c5fdc6f27
King, Ronald C.
d7145079-f066-4995-a92e-6c8a493b734f
Foley, Angèle M.
53e0c35d-e4bb-461d-9638-1d1c5fdc6f27
King, Ronald C.
d7145079-f066-4995-a92e-6c8a493b734f

Foley, Angèle M. and King, Ronald C. (2018) Factorial Q-functions and Tokuyama identities for classical Lie groups. European Journal of Combinatorics, 73, 89-113. (doi:10.1016/j.ejc.2018.05.009).

Record type: Article

Abstract

Factorial characters of each of the classical Lie groups have recently been defined algebraically as rather simple deformations of irreducible characters. Each such factorial character has been shown to satisfy a flagged Jacobi–Trudi identity, thereby allowing for its combinatorial realisation in terms of first a non-intersecting lattice path model and then a tableau model. Here we propose algebraic definitions of factorial Q-functions of the classical Lie groups and translate these definitions into combinatorial realisations in terms of non-intersecting lattice path and primed shifted tableaux models. By way of some justification of our chosen definitions, it is then shown that our factorial Q-functions satisfy Tokuyama-type identities and relate some special case of these to other identities that have appeared in the literature.

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factorial-Q-functions-final-12oct17 - Accepted Manuscript
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Submitted date: 24 October 2017
Accepted/In Press date: 30 May 2018
e-pub ahead of print date: 19 June 2018
Published date: 1 October 2018

Identifiers

Local EPrints ID: 422962
URI: https://eprints.soton.ac.uk/id/eprint/422962
ISSN: 0195-6698
PURE UUID: ef306de3-5ae0-4ec7-b298-71a424b32642

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Date deposited: 08 Aug 2018 16:30
Last modified: 20 Jul 2019 04:12

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