Supercharacter Theory Constructions Corresponding to Schur Ring Products

2012 ◽  
Vol 40 (12) ◽  
pp. 4420-4438 ◽  
Author(s):  
Anders O. F. Hendrickson
Keyword(s):  
Schur Ring ◽  
Supercharacter Theory

scholarly journals An answer to Hirasaka and Muzychuk: Every p-Schur ring over Cp3 is Schurian

2008 ◽  
Vol 308 (9) ◽  
pp. 1760-1763 ◽  
Author(s):  
Pablo Spiga ◽  
Qiang Wang
Keyword(s):  
Schur Ring

scholarly journals SCHUR RING AND QUASI-SIMPLE MODULES

2009 ◽  
Vol 28 (2) ◽  
Author(s):  
Pedro Domínguez-Wade
Keyword(s):  
Simple Modules ◽  
Schur Ring

Supercharacters and mixed moments of Kloosterman sums

2018 ◽  
Vol 14 (04) ◽  
pp. 1023-1032 ◽  
Author(s):  
Ángel Chávez ◽  
George Todd
Keyword(s):  
Elliptic Curve ◽  
Recent Work ◽  
Kloosterman Sums ◽  
Fourth Degree ◽  
Mixed Power ◽  
Power Moments ◽  
Supercharacter Theory ◽  
Trace Of Frobenius

Recent work has realized Kloosterman sums as supercharacter values of a supercharacter theory on [Formula: see text]. We use this realization to express fourth degree mixed power moments of Kloosterman sums in terms of the trace of Frobenius of a certain elliptic curve.

Strong Gelfand pairs of symmetric groups

2020 ◽  
pp. 2150054
Author(s):  
Gradin Anderson ◽  
Stephen P. Humphries ◽  
Nathan Nicholson
Keyword(s):  
Commutative Ring ◽  
Finite Groups ◽  
Symmetric Groups ◽  
Maximal Dimension ◽  
Gelfand Pair ◽  
Gelfand Pairs ◽  
Schur Ring

A strong Gelfand pair is a pair [Formula: see text], of finite groups such that the Schur ring determined by the [Formula: see text]-classes [Formula: see text], is a commutative ring. We find all strong Gelfand pairs [Formula: see text]. We also define an extra strong Gelfand pair [Formula: see text], this being a strong Gelfand pair of maximal dimension, and show that in this case [Formula: see text] must be abelian.

scholarly journals Upper and Lower Semimodularity of the Supercharacter Theory Lattices of Cyclic Groups

2013 ◽  
Vol 42 (3) ◽  
pp. 1123-1135 ◽  
Author(s):  
Samuel G. Benidt ◽  
William R. S. Hall ◽  
Anders O. F. Hendrickson
Keyword(s):  
Cyclic Groups ◽  
Supercharacter Theory

An algorithm for computing a supercharacter theory generated from a given partition

2021 ◽  
pp. 1-12
Author(s):  
Shawn T. Burkett
Keyword(s):  
Finite Group ◽  
Partial Order ◽  
Supercharacter Theory ◽  
A Finite Group

Let [Formula: see text] be a finite group. The set of all supercharacter theories of [Formula: see text] forms a lattice, where the join operation coincides with the join operation on the lattice of partitions of [Formula: see text], with partial order given by refinement. The meet operation is more complicated however, and seems difficult to describe. In this paper, we outline algorithms for determining the coarsest supercharacter theory whose associated partition is finer than a given partition. One of the primary applications is to compute the supercharacters and superclasses for the meet of two supercharacter theories.

Sign in / Sign up

Export Citation Format

Share Document