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Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
- Source :
- Advances in Mathematics, Advances in Mathematics, Elsevier, 2011, 229, pp.2310-2337. ⟨10.1016/j.aim.2011.12.024⟩
- Publisher :
- Elsevier Inc.
-
Abstract
- 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.<br />Comment: To Appear in Advances in Mathematics (2012), 23 pages
- Subjects :
- Mathematics(all)
General Mathematics
Symmetric functions in noncommuting variables
Field (mathematics)
Representation theory of Hopf algebras
0102 computer and information sciences
Unipotent
Quasitriangular Hopf algebra
01 natural sciences
Unipotent uppertriangular matrices
Mathematics::Quantum Algebra
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
FOS: Mathematics
Mathematics - Combinatorics
0101 mathematics
Representation Theory (math.RT)
Ring of symmetric functions
Mathematics
[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]
Quantum group
Combinatorial Hopf algebra
010102 general mathematics
16. Peace & justice
Hopf algebra
Algebra
Symmetric function
Supercharacters
010201 computation theory & mathematics
Finite fields
Combinatorics (math.CO)
05E10
Mathematics - Representation Theory
Subjects
Details
- Language :
- English
- ISSN :
- 00018708 and 10902082
- Issue :
- 4
- Database :
- OpenAIRE
- Journal :
- Advances in Mathematics
- Accession number :
- edsair.doi.dedup.....be8edf90db13b5010a4bd4ece93da33c
- Full Text :
- https://doi.org/10.1016/j.aim.2011.12.024