17 citations · 121 across the 36 of their papers we have counts for
27 papers · 1 filter
Machine-Learning Kronecker Coefficients
Kyu-Hwan Lee
The Kronecker coefficients are the decomposition multiplicities of the tensor product of two irreducible representations of the symmetric group. Unlike the Littlewood--Richardson c…
Braid group action on quantum virtual Grothendieck ring through constructing presentations
Il-Seung Jang, Kyu-Hwan Lee, Se-jin Oh
As a continuation of \cite{JLO1}, we investigate the quantum virtual Grothendieck ring $\frakK_q(\g)$ associated with a finite dimensional simple Lie algebra $\g$, especially of no…
Quantization of virtual Grothendieck rings and their structure including quantum cluster algebras
Il-Seung Jang, Kyu-Hwan Lee, Se-jin Oh
The quantum Grothendieck ring of a certain category of finite-dimensional modules over a quantum loop algebra associated with a complex finite-dimensional simple Lie algebra $\math…
Auto-correlation functions for unitary groups
Kyu-Hwan Lee, Se-jin Oh
We compute the auto-correlations functions of order for the characteristic polynomials of random matrices from certain subgroups of the unitary groups $\U(2)$ and $\U(3)$…
Rigid reflections of rank 3 Coxeter groups and reduced roots of rank 2 Kac--Moody algebras
Kyu-Hwan Lee, Jeongwoo Yu
In a recent paper by K.-H. Lee and K. Lee, rigid reflections are defined for any Coxeter group via non-self-intersecting curves on a Riemann surface with labeled curves. When the C…
Character expansion of Kac-Moody correction factors
Kyu-Hwan Lee, Dongwen Liu, Thomas Oliver
A correction factor naturally arises in the theory of p-adic Kac--Moody groups. In this paper, we expand the correction factor into a sum of irreducible characters of the underlyin…
Quantum generalized Kac--Moody algebras via Hall algebras of complexes
Jonathan D. Axtell, Kyu-Hwan Lee
We establish an embedding of the quantum enveloping algebra of a symmetric generalized Kac--Moody algebra into a localized Hall algebra of -graded complexes of represe…
Geometric description of C-vectors and real Lösungen
Kyu-Hwan Lee, Kyungyong Lee, Matthew R. Mills
We introduce real Loesungen as an analogue of real roots. For each mutation sequence of an arbitrary skew-symmetrizable matrix, we define a family of reflections along with associa…
Some branching formulas for Kac--Moody Lie algebras
Kyu-Hwan Lee, Jerzy Weyman
In this paper we give some branching rules for the fundamental representations of Kac--Moody Lie algebras associated to -shaped graphs. These formulas are useful to describe gen…
Rigid reflections and Kac--Moody algebras
Kyu-Hwan Lee, Kyungyong Lee
Given any Coxeter group, we define rigid reflections and rigid roots using non-self-intersecting curves on a Riemann surface with labeled curves. When the Coxeter group arises from…
Weight multiplicities and Young tableaux through affine crystals
Jang Soo Kim, Kyu-Hwan Lee, Se-jin Oh
The weight multiplicities of finite dimensional simple Lie algebras can be computed individually using various methods. Still, it is hard to derive explicit closed formulas. Simila…
A correspondence between rigid modules over path algebras and simple curves on Riemann surfaces
Kyu-Hwan Lee, Kyungyong Lee
We propose a conjectural correspondence between the set of rigid indecomposable modules over the path algebras of acyclic quivers and the set of certain non-self-intersecting curve…
Representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras
Konstantina Christodoulopoulou, Kyu-Hwan Lee
We construct all the irreducible representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras and show that their highest weights are given by t…
Homogeneous representations of Type A KLR-algebras and Dyck paths
Gabriel Feinberg, Kyu-Hwan Lee
The Khovanov-Lauda-Rouquier (KLR) algebra arose out of attempts to categorify quantum groups. Kleshchev and Ram proved a result reducing the representation theory of these algebras…
A combinatorial approach to root multiplicities of rank 2 hyperbolic Kac-Moody algebras
Seok-Jin Kang, Kyu-Hwan Lee, Kyungyong Lee
In this paper we study root multiplicities of rank 2 hyperbolic Kac-Moody algebras using the combinatorics of Dyck paths.
Fully commutative elements of type D and homogeneous representations of KLR-algebras
Gabriel Feinberg, Kyu-Hwan Lee
In this paper, we decompose the set of fully commutative elements into natural subsets when the Coxeter group is of type , and study the combinatorics of these subsets, reveal…
Dimensions of Imaginary Root Spaces of Hyperbolic Kac--Moody Algebras
Lisa Carbone, Walter Freyn, Kyu-Hwan Lee
We discuss the known results and methods for determining root multiplicities for hyperbolic Kac--Moody algebras.
Eisenstein series on rank 2 hyperbolic Kac--Moody groups
Lisa Carbone, Kyu-Hwan Lee, Dongwen Liu
We define Eisenstein series on rank 2 hyperbolic Kac--Moody groups over R, induced from quasi--characters. We prove convergence of the constant term and hence the almost everywhere…
Rank 2 symmetric hyperbolic Kac-Moody algebras and Hilbert modular forms
Henry H. Kim, Kyu-Hwan Lee
In this paper we study rank two symmetric hyperbolic Kac-Moody algebras H(a) and their automorphic correction in terms of Hilbert modular forms. We associate a family of H(a)'s to…
Eisenstein series on affine Kac-Moody groups over function fields
Kyu-Hwan Lee, Philip Lombardo
H. Garland constructed Eisenstein series on affine Kac-Moody groups over the field of real numbers. He established the almost everywhere convergence of these series, obtained a for…
Young tableaux, canonical bases and the Gindikin-Karpelevich formula
Kyu-Hwan Lee, Ben Salisbury
A combinatorial description of the crystal B(infinity) for finite-dimensional simple Lie algebras in terms of certain Young tableaux was developed by J. Hong and H. Lee. We establi…
A combinatorial description of the affine Gindikin-Karpelevich formula of type A_n^(1)
Seok-Jin Kang, Kyu-Hwan Lee, Hansol Ryu +1
The classical Gindikin-Karpelevich formula appears in Langlands' calculation of the constant terms of Eisenstein series on reductive groups and in Macdonald's work on p-adic groups…
Combinatorics of the Casselman-Shalika formula in type A
Kyu-Hwan Lee, Philip Lombardo, Ben Salisbury
In the recent works of Brubaker-Bump-Friedberg, Bump-Nakasuji, and others, the product in the Casselman-Shalika formula is written as a sum over a crystal. The coefficient of each…
Quantum affine algebras, canonical bases and -deformation of arithmetical functions
Henry H. Kim, Kyu-Hwan Lee
In this paper, we obtain affine analogues of Gindikin-Karpelevich formula and Casselman-Shalika formula as sums over Kashiwara-Lusztig's canonical bases. Suggested by these formula…