29 citations · 40 across the 13 of their papers we have counts for
5 papers · 1 filter
A Fibonacci variant of the Rogers-Ramanujan identities via crystal energy
Shunsuke Tsuchioka
We define a length function for a perfect crystal. As an application, we derive a variant of the Rogers-Ramanujan identities which involves (a -analog of) the Fibonacci numbers.
A proof of the second Rogers-Ramanujan identity via Kleshchev multipartitions
Shunsuke Tsuchioka
We give another proof of the second Rogers-Ramanujan identity by Kashiwara crystals.
A local characterization of regular crystals
Shunsuke Tsuchioka
Stembridge characterized regular crystals associated with a simply-laced generalized Cartan matrix (GCM) in terms of local graph-theoretic quantities. We give a similar axiomatizat…
Schur partition theorems via perfect crystal
Shunsuke Tsuchioka, Masaki Watanabe
Motivated by spin modular representations of the symmetric groups, we propose two generalizations of the Schur regular partitions for an odd integer . One forms a subset o…
Quiver Hecke superalgebras
Seok-Jin Kang, Masaki Kashiwara, Shunsuke Tsuchioka
We introduce a new family of superalgebras which should be considered as a super version of the Khovanov-Lauda-Rouquier algebras. Let be the set of vertices of a Dynkin diagram…