WebFinite reductive groups and their representations lie at the heart of goup theory. After representations of finite general linear groups were determined by Green (1955), the … WebJul 29, 2024 · G. Lusztig, Characters of Reductive Groups Over a Finite Field, Annals of Mathematics Studies, Vol. 107, Princeton University Press, Princeton, NJ, 1984. Lusztig, G.: Remarks on Springer’s representations. Represent. Theory. 13, 391–400 (2009) Article MathSciNet MATH Google Scholar

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WebMar 2, 2016 · irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection cohomology, and detailed information on representations of Weyl groups. Topics General Mathematics Mathematics Access through your institution Add or Change Institution — or — PDF $234.50 Buy PDF WebThese groups, which can be described as the groups you get by taking the points over a finite field of a reductive algebraic groups, include (in a sense) most of the finite … grace community church app

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In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation with finite kernel which is a direct sum of irreducible representations. Reductive groups include some of … See more A linear algebraic group over a field k is defined as a smooth closed subgroup scheme of GL(n) over k, for some positive integer n. Equivalently, a linear algebraic group over k is a smooth affine group scheme over k. See more GLn and SLn A fundamental example of a reductive group is the general linear group $${\displaystyle {\text{GL}}_{n}}$$ of invertible n × n matrices over a field k, for a natural number n. In particular, the multiplicative group … See more For a split reductive group G over a field k, the smooth connected subgroups of G that contain a given Borel subgroup B of G are in one-to-one correspondence with the subsets of the set Δ … See more A group scheme G over a scheme S is called reductive if the morphism G → S is smooth and affine, and every geometric fiber See more Every compact connected Lie group has a complexification, which is a complex reductive algebraic group. In fact, this construction gives a one-to-one correspondence … See more The classification of reductive algebraic groups is in terms of the associated root system, as in the theories of complex semisimple Lie algebras or compact Lie groups. Here is the … See more Chevalley showed in 1958 that the reductive groups over any algebraically closed field are classified up to isomorphism by … See more WebThe theory of group schemes of finite type over a field. CUP 2024, 644pp. v2, 2013, 186pp. v2, 2024, 139pp. The goal of this project is to make it possible for everyone to learn the essential theory of algebraic group schemes (especially reductive groups), Lie algebras, Lie groups, and arithmetic subgroups with the minimum of prerequisites and ... The symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself. Since there are n! (n factorial) possible permutations of a set of n symbols, it follows that the order (the number of elements) of the s… chillcoots