29 citations · 40 across the 13 of their papers we have counts for
11 papers · 1 filter
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)}_…
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…
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…
Andrews-Gordon type series for the level 5 and 7 standard modules of the affine Lie algebra
Motoki Takigiku, Shunsuke Tsuchioka
We give Andrews-Gordon type series for the principal characters of the level 5 and 7 standard modules of the affine Lie algebra . We also give conjectural series for s…
BMR freeness for icosahedral family
Shunsuke Tsuchioka
We verify the Broué-Malle-Rouquier (BMR) freeness for cyclotomic Hecke algebras associated with complex reflection groups , , in the Shephard-Todd classifi…
Pattern avoidance seen in multiplicities of maximal weights of affine Lie algebra representations
Shunsuke Tsuchioka, Masaki Watanabe
We prove that the multiplicities of certain maximal weights of -modules are counted by pattern avoidance on words. This proves and generalizes a conjectu…