Deligne lusztig theory
WebThe theory was clarified by the theory of algebraic groups, and the work of Chevalley on Lie algebras, by means of which the Chevalley group concept was isolated. ... WebDeligne-Lusztig (1976) - Construction of a class of “interesting” varieties Lusztig (1976-77-78-79-80-81-82-83-84) - I Parametrization of irreducible characters I …
Deligne lusztig theory
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WebThe associated affine Deligne–Lusztig varieties Xx(b), which are indexed by elements b∈G(F) and x∈W, were introduced by Rapoport. Basic questions about the ... The final chapters of the book describe the Kashiwara-Lusztig theory of so-called crystal (or canonical) bases in representations of complex semisimple Lie algebras. The choice of ... WebDELIGNE–LUSZTIG THEORY 3 Example1.4.(i)Presheavesofarbitrary,continuous,smooth,orholomorphicfunctionsare …
WebOct 5, 2024 · Affine Deligne-Lusztig Varieties and Quantum Bruhat Graph. In this paper, we consider affine Deligne-Lusztig varieties and their certain union inside the affine flag variety of a reductive group. Several important results in the study of affine Deligne-Lusztig varieties have been established under the so-called superregularity hypothesis. WebThe Deligne-Lusztig theory investigates the representations of the nite groups GF. A key role in this representation theory is played by the maximal tori of G and GF. A torus in G is a closed subgroup isomorphic to a direct product of copies of the multiplicative group of K. Any two maximal tori
WebNov 28, 2024 · Note that there are generalisations of Deligne-Lusztig theory to this setting; 7 see e.g. [Lus04], [Sta11], and [Che18]. Moreover, Weinstein's formula (2) still holds, and there are also possible ... WebClassification of irreducible representations of Hecke algebras (Deligne-Langlands-Lusztig conjecture) in terms of K-theory and perverse sheaves; Applications of D-modules and perverse sheaves to representations of complex or real reductive groups and to semisimple Lie algebras (Kazhdan-Lusztig conjecture);
WebDELIGNE-LUSZTIG THEORY 3 This paper is organized as follows. In section 2, we give a fairly detailed description of the construction of Deligne-Lusztig variety and the virtual representations Rµ T of GF, and try to show that the idea of construction can be naturally understood in terms of the rational structure of the flag variety of G.In sections 3 and 4 …
WebFeb 4, 2024 · (07-04-2024): Section 7 of Deligne-Lusztig (Pol van Hoften) Notes; References. Six lectures on Deligne-Lusztig theory by Raphael Rouquier. The original paper "Representations of reductive groups over finite fields" by Deligne and Lusztig (available here). An introduction to Deligne-Lusztig theory by Teruyoshi Yoshida the tirashanWebWe study the Newton stratification on SL3( F), where F is a Laurent power series field. We provide a formula for the codimensions of the Newton strata inside each component of the affine Bruhat decom the tire choice clearwater fl 33765Deligne and Lusztig's construction is a generalization of parabolic induction to non-split tori using higher cohomology groups. (Parabolic induction can also be done with tori of G replaced by Levi subgroups of G, and there is a generalization of Deligne–Lusztig theory to this case too.) See more In mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support, introduced by Pierre Deligne and George Lusztig See more The construction of Deligne-Lusztig characters uses a family of auxiliary algebraic varieties XT called Deligne–Lusztig varieties, constructed from a reductive linear algebraic group G defined over a finite field Fq. If B is a Borel … See more Suppose that q is an odd prime power, and G is the algebraic group SL2. We describe the Deligne–Lusztig representations of … See more Lusztig (1985) replaced the ℓ-adic cohomology used to define the Deligne-Lusztig representations with intersection ℓ-adic cohomology, and introduced certain perverse sheaves called … See more Suppose that G is a reductive group defined over a finite field, with Frobenius map F. Ian G. Macdonald conjectured … See more • The character of R T does not depend on the choice of prime l≠p, and if θ=1 its values are rational integers. • Every irreducible … See more Lusztig classified all the irreducible characters of G by decomposing such a character into a semisimple character and a unipotent character (of another group) and separately classifying the semisimple and unipotent characters. The dual group See more the tire center burlington ncWebJul 25, 2012 · In 1979 Lusztig proposed a conjectural construction of supercuspidal representations of reductive p-adic groups, which is similar to the well known construction of Deligne and Lusztig in the setting of finite reductive groups. We present a general method for explicitly calculating the representations arising from Lusztig's construction and … the tire center portland inWeb150 12 Deligne-Lusztig Theory: an Overview* Lang’s theorem. If His a connected algebraic group and if F: H→His a Frobe-nius endomorphism of H, then the morphism H→ H, h→ … setting up western digital my cloudWebDELIGNE-LUSZTIG THEORY 3 This paper is organized as follows. In section 2, we give a fairly detailed description of the construction of Deligne-Lusztig variety and the virtual … the tire clinicWebTitle: Deligne-Lusztig Theory. Abstract: The representation theory of G = SL2(C) can be realized in the global sections of Serre's twisting sheaves O(n) on P1. This is a special case of the Borel-Weil-Bott theorem, which relates the representations of complex algebraic groups and the sheaf cohomology of certain vector bundles. setting up westnet email on outlook