36 citations · 131 across the 24 of their papers we have counts for
21 papers · 1 filter
A piecewise-linear formula for rigid representations of Dynkin quivers
Deniz Kus, Markus Reineke
We derive a piecewise-linear formula for the rigid representation of a Dynkin quiver of a given dimension vector, and illustrate the formula in several examples.
Pieri formulas, higher level Demazure crystals and numerical multiplicities of excellent filtrations
Deniz Kus, Valentin Rappel
The classical Pieri formula gives a multiplicity free expansion of an irreducible module with a fundamental one for the complex general linear group. In this article we replace the…
Quantum affine algebras, graded limits, and flags
Matheus Brito, Vyjayanthi Chari, Deniz Kus +1
In this survey, we review some of the recent connections between the representation theory of (untwisted) quantum affine algebras and the representation theory of current algebras.…
Simplified presentations and embeddings of Demazure modules
Deniz Kus, R. Venkatesh
For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g. level one in type A) which…
Prime representations in the Hernandez-Leclerc category: classical decompositions
Leon Barth, Deniz Kus
We use the dual functional realization of loop algebras to study the prime irreducible objects in the Hernandez-Leclerc category for the quantum affine algebra associated to $\math…
Graded decompositions of fusion products in rank two
Leon Barth, Deniz Kus
We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and re…
PBW degenerations of Lie superalgebras and their typical representations
Ghislain Fourier, Deniz Kus
We introduce the PBW degeneration for basic classical Lie superalgebras and construct for all type I, and exceptional Lie superalgebras new monomial bases. T…
A combinatorial formula for graded multiplicities in excellent filtrations
Rekha Biswal, Deniz Kus
A filtration of a representation whose successive quotients are isomorphic to Demazure modules is called an excellent filtration. In this paper we study graded multiplicities in ex…
Borel--de Siebenthal pairs, Global Weyl modules and Stanley--Reisner rings
Vyjayanthi Chari, Deniz Kus, Matt Odell
We develop the theory of integrable representations for an arbitrary maximal parabolic subalgebra of an affine Lie algebra. We see that such subalgebras can be thought of as arisin…
Demazure flags, --Fibonacci polynomials and hypergeometric series
Rekha Biswal, Vyjayanthi Chari, Deniz Kus
We study a family of finite--dimensional representations of the hyperspecial parabolic subalgebra of the twisted affine Lie algebra of type . We prove that these mod…
Representations of Lie superalgebras with fusion flags
Deniz Kus
We study the category of finite--dimensional representations for a basic classical Lie superalgebra $\Lg=\Lg_0\oplus \Lg_1$. For the ortho--symplectic Lie superalgebra $\Lg=\mathfr…
The PBW filtration and convex polytopes in type
Teodor Backhaus, Deniz Kus
We study the PBW filtration on irreducible finite--dimensional representations for the Lie algebra of type . We prove in several cases, including all multiples of the adjo…
Fusion products and toroidal algebras
Deniz Kus, Peter Littelmann
We study the category of finite--dimensional bi--graded representations of toroidal current algebras associated to finite--dimensional complex simple Lie algebras. Using the theory…
Twisted Demazure modules, fusion product decomposition and twisted Q--systems
Deniz Kus, R. Venkatesh
In this paper, we introduce a family of indecomposable finite-dimensional graded modules for the twisted current algebras. These modules are indexed by an -tuple of partitio…
Weyl modules for the hyperspecial current algebra
Vyjayanthi Chari, Bogdan Ion, Deniz Kus
We develop the theory of global and local Weyl modules for the hyperspecial maximal parabolic subalgebra of type . We prove that the dimension of a local Weyl module…
Kirillov-Reshetikhin crystals, energy function and the combinatorial R-matrix
Deniz Kus
We study the polytope model for the affine type Kirillov-Reshetikhin crystals and prove that the action of the affine Kashiwara operators can be described in a remarkable simpl…
Crystal bases as tuples of integer sequences
Deniz Kus
We describe a set consisting of tuples of integer sequences and provide certain explicit maps on it. We show that this defines a semiregular crystal for $\ma…
Realization of affine type A Kirillov-Reshetikhin crystals via polytopes
Deniz Kus
On the polytope defined in Feigin, Fourier, and Littelmann (2011), associated to any rectangle highest weight, we define a structure of an type -crystal. We show, by using the…
Demazure modules and Weyl modules: The twisted current case
Ghislain Fourier, Deniz Kus
We study finite-dimensional respresentations of twisted current algebras and show that any graded twisted Weyl module is isomorphic to level one Demazure module for the twisted aff…
Local Weyl modules for equivariant map algebras with free abelian group actions
Ghislain Fourier, Tanusree Khandai, Deniz Kus +1
Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from X to g.…
Weyl modules for multiloop algebras
Ghislain Fourier, Tanusree Khandai, Deniz Kus
Global and local Weyl modules for the untwisted multiloop Lie algebras were defined by Chari, the first and the second author via homological properties. In this paper we extended…