Abstract
We focus on derangement characters of GL(n,q) which depend solely on the dimension of the space of fixed vectors. This family includes Thoma characters which become asymptotically irreducible as n→∞. We find explicit decomposition of Thoma characters into irreducibles, construct further derangement characters and seek for extremes in the family derangement characters.
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Kirillov, A. N.: Ubiquity of Kostka polynomials, In: Proc. Nagoya Intern. Workshop in Physics and Combinatorics, World Scientific, Singapore, 1999, pp. 85–200 (also available via arXiv:math.QA/9912094).
Kirillov, A. N.: The Lagrange identity and the hook formula, J. Soviet Math. 59 (1992), 1078–1084 (translated from Russian).
Skudlarek, H.-L.: Die unzerlegbaren Charaktere einiger diskreter Gruppen, Math. Ann. 223 (1976), 213–231.
Stanley, R.: Enumerative Combinatorics, Vol. 2, Cambridge University Press, 1999.
Thoma, E.: Characters of the group GL(∞,q), In: Lecture Notes in Math. 266, Springer, New York, 1972, pp. 321–323.
Macdonald, I. G.: Symmetric Functions and Hall Polynomials, Oxford University Press, 1999.
Zelevinsky, A.: Representations of Finite Classical Groups: A Hopf Algebra Approach, Lecture Notes in Math. 869, Springer, New York, 1981.
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Mathematics Subject Classification (2000)
20C15.
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Gnedin, A., Kerov, S. Derangement Characters of the Finite General Linear Group. Algebr Represent Theor 8, 255–274 (2005). https://doi.org/10.1007/s10468-005-0858-x
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DOI: https://doi.org/10.1007/s10468-005-0858-x