Super-characters of finite unipotent groups of types B n , C n and D n

By C. André, Ana Margarida Neto. 2006

59 citations recorded by the source corpus.

Abstract We define and study super-characters (over the complex field) of the classical finite unipotent groups of types B n , C n and D n . Under the assumption that the prime is sufficiently large, we extend the known results for the unitriangular group proved by the first author in the papers: [C.A.M. Andre, Basic characters of the unitriangular group, J. Algebra 175 (1995) 287–319], and [C.A.M. Andre, Basic characters of the unitriangular group (for arbitrary primes), Proc. Amer. Math. Soc. 130 (7) (2002) 1943–1954]. In particular, we prove that every irreducible (complex) character occurs as a constituent of a unique super-character. We also give a combinatorial description of all the irreducible characters of maximum degree.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/482ad122f630e4d3e465f7a3d8262458f42875bb

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Citations in the corpus

A supercharacter theory for the Sylow p-subgroups of the finite symplectic and orthogonal groups (2008, methodology): “In the papers [ 5 ] (for sufficiently large primes) and [6] (for a odd primes), the authors started to develop a supercharacter theory for a Sylow p-subgroup U of one the”
Branching rules in the ring of superclass functions of unipotent upper-triangular matrices (2008, background): “U[2,5] = ⎧ ⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ ⎛ ⎜⎜⎜⎜⎜⎜⎝ 1 0 0 0 0 0 0 0 1 ∗ ∗ ∗ 0 0 0 0 1 ∗ ∗ 0 0 0 0 0 1 ∗ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 ⎞ ⎟⎟⎟⎟⎟⎟⎠ ⎫ ⎪⎪⎪⎪⎪⎬ ⎪⎪⎪⎪⎪⎭ ⊆ ⎧ ⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎩ ⎛ ⎜⎜⎜⎜⎜⎜⎝ 1 ∗ ∗ ∗ ∗ ∗ ∗ 0 1 ∗ ∗ ∗ ∗ ∗ 0 0 1 ∗ ∗ ∗ ∗ 0 0 0 1 ∗ ∗ ∗ 0 0 0 0 1 ∗ ∗ 0 0 0 0 0 1 ∗ 0 0 0 0 0 0 1 ⎞ ⎟⎟⎟⎟⎟⎟⎠ ⎫ ⎪⎪⎪”
Supercharacter formulas for pattern groups (2006, methodology): “Neto have constructed a supercharacter theory for types B, C, and D [5].”