Abstract

We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of Uq(slₑ). These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of the Ext¹ -quivers of v-Schur algebras at complex e-th roots of unity generated by simple modules corresponding to these canonical basis vectors are given by the 1-skeletons of the polytopal complexes.

Publication Type:	Article
Additional Information:	© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Quantised Fock space, Canonical basis, q-decomposition numbers, v-Schur algebras, Parallelotope tilings
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics

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