Toya Hiroshima

activity

20182021

collaborators

4 papers

math.CO2021

Perfectness of Kirillov-Reshetikhin Crystals $B^{r, s}$ for types $E_{6}^{(1)}$ and $E_{7}^{(1)}$ with a minuscule node $r$

Toya Hiroshima

We prove the perfectness of Kirillov-Reshetikhin crystals $B^{r, s}$ for types $E_{6}^{(1)}$ and $E_{7}^{(1)}$ with $r$ being the minuscule node and $s \geq 1$ using the polytope mod…

math.CO2021

An Explicit Algorithm of Rigged Configuration Bijection for the Adjoint Crystal of Type $G_{2}^{(1)}$

Toya Hiroshima

We construct an explicit algorithm of the static-preserving bijection between the rigged configurations and the highest weight paths of the form $(B^{2, 1})^{\otimes L}$ in the $G_{…

math.CO2019

Queer Supercrystal Structure for Increasing Factorizations of Fixed-Point-Free Involution Words

Toya Hiroshima

We show that the set of increasing factorizations of fixed-point-free (FPF) involution words has the structure of queer supercrystals. By exploiting the algorithm of symplectic shi…

math.CO2018

$q$ -crystal structure on primed tableaux and on signed unimodal factorizations of reduced words of type $B$

Toya Hiroshima

Crystal basis theory for the queer Lie superalgebra was developed by Grantcharov et al. and it was shown that semistandard decomposition tableaux admit the structure of crystals fo…

Perfectness of Kirillov-Reshetikhin Crystals Br,s for types E6(1)​ and E7(1)​ with a minuscule node r

An Explicit Algorithm of Rigged Configuration Bijection for the Adjoint Crystal of Type G2(1)​

Queer Supercrystal Structure for Increasing Factorizations of Fixed-Point-Free Involution Words

q-crystal structure on primed tableaux and on signed unimodal factorizations of reduced words of type B

Perfectness of Kirillov-Reshetikhin Crystals $B^{r, s}$ for types $E_{6}^{(1)}$ and $E_{7}^{(1)}$ with a minuscule node $r$

An Explicit Algorithm of Rigged Configuration Bijection for the Adjoint Crystal of Type $G_{2}^{(1)}$

$q$ -crystal structure on primed tableaux and on signed unimodal factorizations of reduced words of type $B$