105 citations · 532 across the 58 of their papers we have counts for
19 papers · 1 filter
Square root crystals and the square root of
Eric Marberg, Travis Scrimshaw
We introduce a general monoidal category of -root crystals and then study the special case of square root -crystals. The latter objects include Yu's cr…
Classical double Grothendieck transitions
Eric Marberg
Kirillov and Naruse have constructed double Grothendieck polynomials to represent the equivariant K-theory classes of Schubert varieties in the complete flag manifolds of types B,…
Brion atoms for classical types
Eric Marberg
Let be a classical group defined over the complex numbers with a Borel subgroup . Choose a holomorphic involution of and let be its set of fixed points. The group $K…
Perfect models for finite Coxeter groups
Eric Marberg, Yifeng Zhang
A model for a finite group is a set of linear characters of subgroups that can be induced to obtain every irreducible character exactly once. A perfect model for a finite Coxeter g…
Highest weight crystals for Schur Q-functions
Eric Marberg, Kam Hung Tong
Work of Grantcharov et al. develops a theory of abstract crystals for the queer Lie superalgebra . Such -crystals form a monoidal category in which…
Gelfand -graphs for classical Weyl groups
Eric Marberg, Yifeng Zhang
A Gelfand model for an algebra is a module given by a direct sum of irreducible submodules, with every isomorphism class of irreducible modules represented exactly once. We introdu…
Bar operators for quasiparabolic conjugacy classes in a Coxeter group
Eric Marberg
The action of a Coxeter group on the set of left cosets of a standard parabolic subgroup deforms to define a module of the group's Iwahori-Hecke algebra $\mathc…
Comparing and characterizing some constructions of canonical bases from Coxeter systems
Eric Marberg
The Iwahori-Hecke algebra of a Coxeter system has a "standard basis" indexed by the elements of and a "bar involution" given by a certain antilinear map.…
Positivity conjectures for Kazhdan-Lusztig theory on twisted involutions: the finite case
Eric Marberg
Let be any Coxeter system and let be an involution of which preserves the set of simple generators . Lusztig and Vogan have shown that the correspond…
Positivity conjectures for Kazhdan-Lusztig theory on twisted involutions: the universal case
Eric Marberg
Let be a Coxeter system and let be an involution of which preserves the set of simple generators . Lusztig and Vogan have recently shown that the set…
How to compute the Frobenius-Schur indicator of a unipotent character of a finite Coxeter system
Eric Marberg
For each finite, irreducible Coxeter system , Lusztig has associated a set of "unipotent characters" $\Uch(W)$. There is also a notion of a "Fourier transform" on the space…
Exotic characters of unitriangular matrix groups
Eric Marberg
Let $\UT_n(q)$ denote the unitriangular group of unipotent upper triangular matrices over a finite field with cardinality and prime characteristic . It has been…
Combinatorial methods of character enumeration for the unitriangular group
Eric Marberg
Let $\UT_n(q)$ denote the group of unipotent upper triangular matrices over a field with elements. The degrees of the complex irreducible characters of $\UT_n(q)$ a…
Iterative character constructions for algebra groups
Eric Marberg
We construct a family of orthogonal characters of an algebra group which decompose the supercharacters defined by Diaconis and Isaacs. Like supercharacters, these characters are gi…
Generalized Involution Models for Wreath Products
Eric Marberg
We prove that if a finite group has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product also has a generalized involution model…
Automorphisms and Generalized Involution Models of Finite Complex Reflection Groups
Eric Marberg
We prove that a finite complex reflection group has a generalized involution model, as defined by Bump and Ginzburg, if and only if each of its irreducible factors is either $G(r,p…
Superclasses and supercharacters of normal pattern subgroups of the unipotent upper triangular matrix group
Eric Marberg
Let denote the group of unipotent upper-triangular matrices over a fixed finite field $\FF_q$, and let $U_\cP$ denote the pattern subgroup of corresponding…
A Supercharacter Analogue for Normality
Eric Marberg
Diaconis and Isaacs define a supercharacter theory for algebra groups over a finite field by constructing certain unions of conjugacy classes called superclasses and certain reduci…
Superinduction for pattern groups
Eric Marberg, Nathaniel Thiem
It is well-known that the representation theory of the finite group of unipotent upper-triangular matrices over a finite field is a wild problem. By instead considering appro…