scholarly journals A first guide to the character theory of finite groups of Lie type

2018 ◽  
pp. 63-106 ◽  
Author(s):  
Meinolf Geck
Keyword(s):  
Finite Groups ◽  
Character Theory ◽  
Groups Of Lie Type

scholarly journals A sharp upper bound for the size of Lusztig series

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Christine Bessenrodt ◽  
Alexandre Zalesski
Keyword(s):  
Finite Groups ◽  
Upper Bound ◽  
Simple Formula ◽  
Character Theory ◽  
Classical Groups ◽  
Irreducible Characters ◽  
Maximal Size ◽  
Groups Of Lie Type

AbstractThe paper is concerned with the character theory of finite groups of Lie type. The irreducible characters of a group 𝐺 of Lie type are partitioned in Lusztig series. We provide a simple formula for an upper bound of the maximal size of a Lusztig series for classical groups with connected center; this is expressed for each group 𝐺 in terms of its Lie rank and defining characteristic. When 𝐺 is specified as G(q) and 𝑞 is large enough, we determine explicitly the maximum of the sizes of the Lusztig series of 𝐺.

scholarly journals Gelfand–Graev Characters of the Finite Unitary Groups

10.37236/235 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Nathaniel Thiem ◽  
C. Ryan Vinroot
Keyword(s):  
Finite Groups ◽  
Unitary Group ◽  
Symmetric Functions ◽  
Point Of View ◽  
Unitary Groups ◽  
Character Theory ◽  
Characteristic Map ◽  
Finite Unitary Groups ◽  
Combinatorial Point ◽  
Groups Of Lie Type

Gelfand–Graev characters and their degenerate counterparts have an important role in the representation theory of finite groups of Lie type. Using a characteristic map to translate the character theory of the finite unitary groups into the language of symmetric functions, we study degenerate Gelfand–Graev characters of the finite unitary group from a combinatorial point of view. In particular, we give the values of Gelfand–Graev characters at arbitrary elements, recover the decomposition multiplicities of degenerate Gelfand–Graev characters in terms of tableau combinatorics, and conclude with some multiplicity consequences.

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