8 citations · 31 across the 12 of their papers we have counts for
14 papers
Special Kirillov-Reshetikhin crystals
Il-Seung Jang, Travis Scrimshaw
We give a uniform realization of Kirillov-Reshetikhin crystals , in terms of PBW crystals, for all affine types, , and nodes in the orbit of the node in…
Unipotent quantum coordinate ring and minuscule prefundamental representations: twisted case
Il-Seung Jang
We study the prefundamental modules over the Borel subalgebras of the twisted quantum loop algebras, which are introduced by Wang. A character formula for $L_{s,a}^…
Crystal base of the negative half of quantum orthosymplectic superalgebra
Il-Seung Jang, Jae-Hoon Kwon, Akito Uruno
We construct a crystal base of the negative half of a quantum orthosymplectic superalgebra. It can be viewed as a limit of the crystal bases of -deformed irreducible oscillator…
Unipotent quantum coordinate ring and cominuscule prefundamental representations
Il-Seung Jang, Jae-Hoon Kwon, Euiyong Park
We continue the study of realization of the prefundamental modules , introduced by Hernandez and Jimbo, in terms of unipotent quantum coordinate rings as in [J-Kwon-…
Crystal bases of parabolic Verma modules over the quantum orthosymplectic superalgebras
Il-Seung Jang, Jae-Hoon Kwon, Akito Uruno
We show that there exists a unique crystal base of a parabolic Verma module over a quantum orthosymplectic superalgebra, which is induced from a -analogue of a polynomial repres…
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…
Path description for -characters of fundamental modules in type
Il-Seung Jang
In this paper, we investigate the behavior of monomials in the -characters of the fundamental modules over a quantum affine algebra of untwisted type C. As a result, we give sim…
Crystal base of the negative half of the quantum superalgebra
Il-Seung Jang, Jae-Hoon Kwon, Akito Uruno
We construct a crystal base of , the negative half of the quantum superalgebra . We give a combinatorial description of the asso…
A combinatorial realization of Kirillov-Reshetikhin crystals for type E arising from translations
Il-Seung Jang
The main purpose of this paper is to give a combinatorial realization of Kirillov-Reshetikhin (KR simply) crystals for type with a minuscule node …
Unipotent quantum coordinate ring and prefundamental representations for types and
Il-Seung Jang, Jae-Hoon Kwon, Euiyong Park
We give a new realization of the prefundamental representations introduced by Hernandez and Jimbo, when the quantum loop algebra is of types $A_n^…
Lusztig data of Kashiwara-Nakashima tableaux in type D
Il-Seung Jang, Jae-Hoon Kwon
We describe the embedding from the crystal of Kashiwara-Nakashima tableaux in type of an arbitrary shape into that of -Lusztig data associated to a family of reduce…
Flagged Littlewood-Richardson tableaux and branching rule for classical groups
Il-Seung Jang, Jae-Hoon Kwon
We give a new formula for the branching rule from to generalizing the Littlewood's restriction formula. The formula is given in terms of Littlewood-Richard…
Quantum nilpotent subalgebras of classical quantum groups and affine crystals
Il-Seung Jang, Jae-Hoon Kwon
We study the crystal of quantum nilpotent subalgebra of associated to a maximal Levi subalgebra of type . We show that it has an affine crystal structure of typ…