Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Thiem, Nathaniel"'
Autor:
Aliniaeifard, Farid, Thiem, Nathaniel
Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structure via the representation theory of families of algebras. This paper exa
Externí odkaz:
http://arxiv.org/abs/2111.03131
Autor:
Aliniaeifard, Farid, Thiem, Nathaniel
Publikováno v:
Adv. Math. 383 (2021), 107675
There is a long tradition of categorifying combinatorial Hopf algebras by the modules of a tower of algebras (or even better via the representation theory of a tower of groups). From the point of view of combinatorics, such a categorification supplie
Externí odkaz:
http://arxiv.org/abs/1909.01418
Autor:
Aliniaeifard, Farid, Thiem, Nathaniel
The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two canonical bases
Externí odkaz:
http://arxiv.org/abs/1810.01826
Autor:
Aliniaeifard, Farid, Thiem, Nathaniel
The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between groups. A
Externí odkaz:
http://arxiv.org/abs/1810.01353
Autor:
Aliniaeifard, Farid, Thiem, Nathaniel
Publikováno v:
In Advances in Mathematics 4 June 2021 383
Autor:
Thiem, Nathaniel
Even with the introduction of supercharacter theories, the representation theory of many unipotent groups remains mysterious. This paper constructs a family of supercharacter theories for normal pattern groups in a way that exhibit many of the combin
Externí odkaz:
http://arxiv.org/abs/1512.03446
Autor:
Andrews, Scott, Thiem, Nathaniel
Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, generalized Gelfand--Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of th
Externí odkaz:
http://arxiv.org/abs/1505.00763
Autor:
Aliniaeifard, Farid, Thiem, Nathaniel
Publikováno v:
In Journal of Combinatorial Theory, Series A May 2020 172
Autor:
Bragg, Daniel, Thiem, Nathaniel
The maximal subgroup of unipotent upper-triangular matrices of the finite general linear groups are a fundamental family of $p$-groups. Their representation theory is well-known to be wild, but there is a standard supercharacter theory, replacing irr
Externí odkaz:
http://arxiv.org/abs/1405.2299
Publikováno v:
Journal of Algebraic Combinatorics, Volume 40, Issue 4, pp 903-938 (2014)
From a recent paper, we recall the Hopf monoid structure on the supercharacters of the unipotent uppertriangular groups over a finite field. We give cancelation free formula for the antipode applied to the bases of class functions and power sum funct
Externí odkaz:
http://arxiv.org/abs/1302.0865