Parallelotope tilings and q-decomposition numbers

We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of Uq(slˆe). 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 generat...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2017-12, Vol.321, p.80-159
Main Authors: Chuang, Joseph, Miyachi, Hyohe, Tan, Kai Meng
Format: Article
Language:English
Subjects:
Canonical basis
Parallelotope tilings
q-decomposition numbers
Quantised Fock space
v-Schur algebras
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Summary:We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of Uq(slˆe). 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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2017.09.024