29 citations · 40 across the 13 of their papers we have counts for
18 papers
A generalization of partition identities of Göllnitz-Gordon, Rogers-Ramanujan and Nandi
Motoki Takigiku, Shunsuke Tsuchioka
We propose Andrews-Gordon type series for certain level 2 standard modules of type , and prove the corresponding sum-product identities except for $A^{(2)}_…
Remarks on the conjectures of Capparelli, Meurman, Primc and Primc
Shashank Kanade, Matthew C. Russell, Shunsuke Tsuchioka +1
In a series of two papers, S. Capparelli, A. Meurman, A. Primc, M. Primc (CMPP) and then M. Primc put forth three remarkable sets of conjectures, stating that the generating functi…
A vertex operator reformulation of the Kanade-Russell conjecture modulo 9
Shunsuke Tsuchioka
We reformulate the Kanade-Russell conjecture modulo 9 via the vertex operators for the level 3 standard modules of type . Along the same line, we arrive at three parti…
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.
An example of Rogers-Ramanujan bipartition identities of level 3
Shunsuke Tsuchioka
We give manifestly positive Andrews-Gordon type series for the level 3 standard modules of the affine Lie algebra of type . We also give corresponding bipartition identi…