Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
Copyright policy )Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.
To Appear in Advances in Mathematics (2012), 23 pages
- Hong Kong University of Science and Technology China (People's Republic of)
- University of Wisconsin–Oshkosh United States
- Massachusetts Institute of Technology United States
- California Institute of Technology United States
- University of Mary United States
Ordinary representations and characters, Mathematics(all), Symmetric functions in noncommuting variables, Connections of Hopf algebras with combinatorics, 510, Unipotent uppertriangular matrices, FOS: Mathematics, Mathematics - Combinatorics, [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], Representation Theory (math.RT), Symmetric functions and generalizations, Combinatorial Hopf algebra, supercharacters, unipotent, combinatorial Hopf algebra, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Supercharacters, Combinatorial aspects of representation theory, Finite fields, Combinatorics (math.CO), finite fields, symmetric functions in noncommuting variables, 05E10, Mathematics - Representation Theory
Ordinary representations and characters, Mathematics(all), Symmetric functions in noncommuting variables, Connections of Hopf algebras with combinatorics, 510, Unipotent uppertriangular matrices, FOS: Mathematics, Mathematics - Combinatorics, [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], Representation Theory (math.RT), Symmetric functions and generalizations, Combinatorial Hopf algebra, supercharacters, unipotent, combinatorial Hopf algebra, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Supercharacters, Combinatorial aspects of representation theory, Finite fields, Combinatorics (math.CO), finite fields, symmetric functions in noncommuting variables, 05E10, Mathematics - Representation Theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).45 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!