Parallelotope tilings and q-decomposition numbers

Chuang, J., Miyachi, H. & Tan, K. M. (2017). Parallelotope tilings and q-decomposition numbers. Advances in Mathematics, 321, pp. 80-159. doi: 10.1016/j.aim.2017.09.024

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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.

Item Type: Article
Additional Information: © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Uncontrolled Keywords: Quantised Fock space, Canonical basis, q-decomposition numbers, v-Schur algebras, Parallelotope tilings
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science

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