3 results
A parametrization of sheets of conjugacy classes in bad characteristic
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- Journal:
- Canadian Mathematical Bulletin / Volume 66 / Issue 3 / September 2023
- Published online by Cambridge University Press:
- 26 January 2023, pp. 976-983
- Print publication:
- September 2023
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Let G be a simple algebraic group of adjoint type over an algebraically closed field k of bad characteristic. We show that its sheets of conjugacy classes are parametrized by G-conjugacy classes of pairs
$(M,{\mathcal O})$ where M is the identity component of the centralizer of a semisimple element in G and 
${\mathcal O}$ is a rigid unipotent conjugacy class in M, in analogy with the good characteristic case.
Hecke action on the principal block
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- Journal:
- Compositio Mathematica / Volume 158 / Issue 5 / May 2022
- Published online by Cambridge University Press:
- 19 July 2022, pp. 953-1019
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- May 2022
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In this paper we construct an action of the affine Hecke category (in its ‘Soergel bimodules’ incarnation) on the principal block of representations of a simply connected semisimple algebraic group over an algebraically closed field of characteristic bigger than the Coxeter number. This confirms a conjecture of G. Williamson and the second author, and provides a new proof of the tilting character formula in terms of antispherical
$p$-Kazhdan–Lusztig polynomials.
A Generalisation of Nagata's Theorem on Ruled Surfaces
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- Journal:
- Compositio Mathematica / Volume 127 / Issue 3 / July 2001
- Published online by Cambridge University Press:
- 04 December 2007, pp. 321-332
- Print publication:
- July 2001
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