Quadratic elements in unipotent linear groups
نویسندگان
چکیده
منابع مشابه
Quadratic Unipotent Blocks in General Linear, Unitary and Symplectic Groups
An irreducible ordinary character of a finite reductive group is called quadratic unipotent if it corresponds under Jordan decomposition to a semisimple element s in a dual group such that s = 1. We prove that there is a bijection between, on the one hand the set of quadratic unipotent characters of GL(n, q) or U(n, q) for all n ≥ 0 and on the other hand, the set of quadratic unipotent characte...
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Hence, it is easy to count the orbits of GL n q under the conjugation action of U n q but seems hard to do the same for the group U n q itself! We fix some further notation. Let V n q be the vector space of column vectors, a module for GL n q . Recall that a flag is a totally ordered set of n− 1 nonzero proper subspaces of V n q . For g in GL n q let f g be the number of flags fixed by g, so it...
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0.1. Let k be an algebraically closed field of characteristic exponent p ≥ 1. Let G be a reductive connected algebraic group over k. Let U be the variety of unipotent elements of G. The unipotent classes of G are the orbits of the conjugation action of G on U . The theory of Dynkin and Kostant [Ko] provides a classification of unipotent classes of G assuming that p = 1. It is known that this cl...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1972
ISSN: 0021-8693
DOI: 10.1016/0021-8693(72)90077-4