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Character Levels and Character Bounds. II
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 in a logarithmic sense. We strengthen the results of [GLT]
and extend them to all groups of classical type
Stanley character polynomials
Stanley considered suitably normalized characters of the symmetric groups on
Young diagrams having a special geometric form, namely multirectangular Young
diagrams. He proved that the character is a polynomial in the lengths of the
sides of the rectangles forming the Young diagram and he conjectured an
explicit form of this polynomial. This Stanley character polynomial and this
way of parametrizing the set of Young diagrams turned out to be a powerful tool
for several problems of the dual combinatorics of the characters of the
symmetric groups and asymptotic representation theory, in particular to Kerov
polynomials.Comment: Dedicated to Richard P. Stanley on the occasion of his seventieth
birthda
Parafermionic character formulae
We study various aspects of parafermionic theories such as the precise field
content, a description of a basis of states (that is, the counting of
independent states in a freely generated highest-weight module) and the
explicit expression of the parafermionic singular vectors in completely
irreducible modules. This analysis culminates in the presentation of new
character formulae for the parafermionic primary fields. These characters
provide novel field theoretical expressions for \su(2) string functions.Comment: Harvmac (b mode : 37 p
Large character sums
Assuming the Generalized Riemann Hypothesis, the authors study when a
character sum over all n <= x is o(x); they show that this holds if log x / log
log q -> infinity and q -> infinity (q is the size of the finite field).Comment: Abstract added in migration
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