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A plactic algebra action on bosonic particle configurations

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Meinel,  Joanna
Max Planck Institute for Mathematics, Max Planck Society;

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Meinel, J. (2021). A plactic algebra action on bosonic particle configurations. Algebras and Representation Theory, 24(6), 1607-1623. doi:10.1007/s10468-020-10006-w.


Cite as: https://hdl.handle.net/21.11116/0000-0007-8369-F
Abstract
We study the plactic algebra and its action on bosonic particle
configurations in the classical case. These particle configurations together
with the action of the plactic generators can be identified with crystals of
the quantum analogue of the symmetric tensor representations in type A. It
turns out that this action factors over a quotient algebra that we call partic
algebra, whose induced action on bosonic particle configurations is faithful.
We describe a basis of the partic algebra explicitly in terms of a normal form
for monomials, and we compute the center of the partic algebra.