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Register a new userCharacter Levels and Character Bounds. II
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This paper is a continuation of [GLT], which develops a level theory and establishes strong character bounds for finite simple groups of linear and unitary type in the case that the centralizer of the element has small order compared to $|G|$ in a logarithmic sense. We strengthen the results of [GLT] and extend them to all groups of classical type.
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We study connections between the topology of generic character varieties of fundamental groups of punctured Riemann surfaces, Macdonald polynomials, quiver representations, Hilbert schemes on surfaces, modular forms and multiplicities in tensor products of irreducible characters of finite general linear groups.
In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero.
This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character tables of sporadic simple groups.
Let $U$ be a Sylow $p$-subgroup of the finite Chevalley group of type $D_4$ over the field of $q$ elements, where $q$ is a power of a prime $p$. We describe a construction of the generic character table of $U$.
We establish a Springer correspondence for classical symmetric pairs making use of Fourier transform, a nearby cycle sheaf construction and parabolic induction. In particular, we give an explicit description of character sheaves for classical symmetric pairs.
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