12 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…