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arXiv · 1703.05898

Billiards and Tilting Characters for ${\rm SL}_3$

George Lusztig·Geordie Williamson
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Abstract

We formulate a conjecture for the second generation characters of indecomposable tilting modules for ${\rm SL}_3$. This gives many new conjectural decomposition numbers for symmetric groups. Our conjecture can be interpreted as saying that these characters are governed by a discrete dynamical system ("billiards bouncing in alcoves"). The conjecture implies that decomposition numbers for symmetric groups display (at least) exponential growth.

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BibTeXRIS

George Lusztig, Geordie Williamson. 2017-03-17. Billiards and Tilting Characters for ${\rm SL}_3$. https://doi.org/10.3842/sigma.2018.015

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