Counting conjugacy classes in the unipotent radical of parabolic subgroups of GLn(q)
نویسندگان
چکیده
منابع مشابه
COUNTING CONJUGACY CLASSES IN THE UNIPOTENT RADICAL OF PARABOLIC SUBGROUPS OF GLn(q)
Let q be a power of a prime p. Let P be a parabolic subgroup of the general linear group GLn(q) that is the stabilizer of a flag in F n q of length at most 5, and let U = Op(P ). In this note we prove that, as a function of q, the number k(U) of conjugacy classes of U is a polynomial in q with integer coefficients.
متن کاملConjugacy Classes in Maximal Parabolic Subgroups of General Linear Groups
We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a “matrix problem”. Such problems involve finding normal forms for matrices under a specified set of row and column operations. We solve the relevant matrix problem in small dimensional cases. This gives us all conjugacy classes in maximal parabolic subgroups over a ...
متن کاملCounting for conjugacy classes of subgroups in finitely generated group ∗
A new general formula for calculation of number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.
متن کاملCounting Conjugacy Classes of Cyclic Subgroups for Fusion Systems
We give another proof of an observation of Thévenaz [4] and present a fusion system version of it. Namely, for a saturated fusion system F on a finite p-group S, we show that the number of the F-conjugacy classes of cyclic subgroups of S is equal to the rank of certain square matrices of numbers of orbits, coming from characteristic bisets, the characteristic idempotent and finite groups realiz...
متن کاملInduced conjugacy classes, prehomogeneous varieties, and canonical parabolic subgroups
We prove the properties of induced conjugacy classes, without using the original proof by Lusztig and Spaltenstein in the unipotent case, by adapting Borho’s simpler arguments for induced adjoint orbits. We study properties of equivariant fibrations of prehomogeneous affine spaces, especially the existence of relative invariants. We also detect prehomogeneous affine spaces as subquotients of ca...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2010
ISSN: 0030-8730
DOI: 10.2140/pjm.2010.245.47