63 citations · 131 across the 29 of their papers we have counts for
7 papers · 1 filter
Shifted tableaux and products of Schur's symmetric functions
Keiichi Shigechi
We introduce a new combinatorial object, semistandard increasing decomposition tableau and study its relation to a semistandard decomposition tableau introduced by Kraśkiewicz and…
Ballot tilings and increasing trees
Keiichi Shigechi
We study enumerations of Dyck and ballot tilings, which are tilings of a region determined by two Dyck or ballot paths. We give bijective proofs to two formulae of enumerations of…
Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation
Keiichi Shigechi
We construct Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation for on the parabolic Kazhdan--Lusztig bases.…
A Positive integral property on the ground state of the two-boundary Temperley--Lieb Hamiltonian
Keiichi Shigechi
We study the two-boundary Temperley--Lieb loop model on Kazhdan--Lusztig bases of type A and B. We obtain explicit expressions of the ground state of the two-boundary Temper…
Canonical bases of a coideal subalgebra in
Keiichi Shigechi
We consider tensor products of finite-dimensional representations of a coideal subalgebra in . We present an explicit expression for the dual of the canonic…
A new current algebra and the reflection equation
P. Baseilhac, K. Shigechi
We establish an explicit algebra isomorphism between the quantum reflection algebra for the R-matrix and a new type of current algebra. These two algebras are sho…