The ABC of p-cells

• Lars Thorge Jensen ^[1]
  1. [1] Université Clermont Auvergne, Francia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
• Idioma: inglés
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• Resumen

  • Parallel to the very rich theory of Kazhdan–Lusztig cells in characteristic 0, we try to build a similar theory in positive characteristic. We study cells with respect to the p-canonical basis of the Hecke algebra of a crystallographic Coxeter system (see Jensen and Williamson in Categorification and higher representation theory, American Mathematical Society, Providence, 2017). Our main technical tools are the star-operations introduced by Kazhdan–Lusztig (Invent. Math. 53(2):65–184, 1979) which have interesting numerical consequences for the p-canonical basis. As an application, we explicitly describe p-cells in finite type A (i.e. for symmetric groups) using the Robinson–Schensted correspondence. Moreover, we show that Kazhdan–Lusztig cells in finite types B and C decompose into p-cells for p>2.