The canonical compactification of a finite group of Lie type

Abstract. Let M be a reductive monoid with unit group G. Let denote the idempotent cross-section of the G × G-orbits on M. If W is the Weyl group of G and e, f ∈ with e ≤ f , we introduce a projection map from WeW to WfW. We use these projection maps to obtain a new description of the Bruhat-Chevalley order on the Renner monoid of M. For the canonical compactification X of a semisimple group G 0 with Borel subgroup B 0 of G 0 , we show that the poset of B 0 × B 0 -orbits of X (with respect to Zariski closure inclusion) is Eulerian.

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“…Renner and the author [22] obtained an analogue of the canonical monoid M for any finite group G of Lie type.…”

Section: Monoid Hecke Algebras 3519mentioning

confidence: 99%

Monoid Hecke algebras

Putcha

1997

Trans. Amer. Math. Soc.

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Abstract. This paper concerns the monoid Hecke algebras H introduced by Louis Solomon. We determine explicitly the unities of the orbit algebras associated with the two-sided action of the Weyl group W . We use this to:1. find a description of the irreducible representations of H, 2. find an explicit isomorphism between H and the monoid algebra of the Renner monoid R, 3. extend the Kazhdan-Lusztig involution and basis to H, and 4. prove, for a W × W orbit of R, the existence (conjectured by Renner) of generalized Kazhdan-Lusztig polynomials.

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The canonical compactification of a finite group of Lie type

Cited by 27 publications

References 14 publications

The Lattice of J-Classes of (J,σ)-Irreducible Monoids, II

The Lattice of J-Classes of (J,σ)-Irreducible Monoids, II

Bruhat-Chevalley Order in Reductive Monoids

Monoid Hecke algebras

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