5 citations · 15 across the 15 of their papers we have counts for
16 papers
-Kreweras numbers for coincidental Coxeter groups attached to limit symbols
Dongkwan Kim
For a coincidental Coxeter group, i.e. of type or , we define the corresponding -Kreweras numbers attached to limit symbols in the sense of Shoji.…
Sign insertion and Kazhdan-Lusztig cells of affine symmetric groups
Dongkwan Kim, Pavlo Pylyavskyy
Combinatorics of Kazhdan-Lusztig cells in affine type was originally developed by Lusztig, Shi, and Xi. Building on their work, Chmutov, Pylyavskyy, and Yudovina introduced the…
Robinson-Schensted correspondence for unit interval orders
Dongkwan Kim, Pavlo Pylyavskyy
The Stanley-Stembridge conjecture associates a symmetric function to each natural unit interval order . In this paper, we define relations à la Knuth on the symmetric g…
On total Springer representations for the symplectic Lie algebra in characteristic 2 and the exotic case
Dongkwan Kim
Let be the Weyl group of type . We first provide restriction formulas of the total Springer representations for the symplectic Lie algebra in characteristic 2 and the exo…
Two-row -graphs in affine type
Dongkwan Kim, Pavlo Pylyavskyy
For affine symmetric groups we construct finite -graphs corresponding to two-row shapes, and prove their uniqueness. This gives the first non-trivial family of examples of finit…
Asymptotic Hecke algebras and Lusztig-Vogan bijection via affine matrix-ball construction
Dongkwan Kim, Pavlo Pylyavskyy
Affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of Robinson-Schensted correspondence. We sh…
On the Betti numbers of Springer fibers for classical types
Dongkwan Kim
For a Weyl group of classical type, we present a formula to calculate the restriction of (graded) Springer representations of to a maximal parabolic subgroup where the…
An affine generalization of evacuation
M. Chmutov, G. Frieden, D. Kim +2
We establish the existence of an involution on tabloids that is analogous to Schutzenberger's evacuation map on standard Young tableaux. We find that the number of its fixed points…
On the affine Schützenberger involution
Dongkwan Kim
We consider an involution on the affine Weyl group of type induced from the nontrivial automorphism on the (finite) Dynkin diagram. We prove that the number of left cells fixed…
Springer fibers for the minimal and the minimal special nilpotent orbits
Dongkwan Kim
We describe Springer fibers corresponding to the minimal and minimal special nilpotent orbits of simple Lie algebras. As a result, we give an answer to the conjecture of Humphreys…
On total Springer representations for classical types
Dongkwan Kim
We give explicit formulas on total Springer representations for classical types. We also describe the characters of restrictions of such representations to a maximal parabolic subg…
Euler Characteristic of Springer fibers
Dongkwan Kim
For Weyl groups of classical types, we present formulas to calculate the restriction of Springer representations to a maximal parabolic subgroup of the same type. As a result, we g…
Stability of Springer representations for type
Dongkwan Kim
We prove certain stability properties of Springer representations for type .
Euler characteristic of analogues of a Deligne-Lusztig variety for
Dongkwan Kim
In this paper we give a combinatorial formula to calculate the Euler characteristic of an analogue of a Deligne-Lusztig variety if we replace Frobenius morphism with conjugation by…
A Comparison of Two Complexes
Dongkwan Kim
In this paper we prove the conjecture of Lusztig in "Generic character sheaves on groups over ." Given a reductive group over for some …
Homology Class of a Deligne-Lusztig variety and its analogues
Dongkwan Kim
In this paper we consider Deligne-Lusztig varieties and their analogues when the Frobenius endomorphism is replaced with conjugation by an element in a group, especially a regular…