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Billiards and Tilting Characters for $\mathrm{SL}_3$
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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We formulate a conjecture for the second generation characters of indecomposable tilting modules for $\mathrm{SL}_3$. 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.
Keywords: tilting modules; billiards; $p$-canonical basis; symmetric group. 
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     author = {George Lusztig and Geordie Williamson},
     title = {Billiards and {Tilting} {Characters} for $\mathrm{SL}_3$},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a14/}
}
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George Lusztig; Geordie Williamson. Billiards and Tilting Characters for $\mathrm{SL}_3$. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a14/

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