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of 60
pro vyhledávání: '"Tsuchioka, Shunsuke"'
In a sequence 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 functions of coloured integer partition in which the parts satisfy restric
Externí odkaz:
http://arxiv.org/abs/2404.03851
Autor:
Tsuchioka, Shunsuke
We reformulate the Kanade-Russell conjecture modulo 9 via the vertex operators for the level 3 standard modules of type $D^{(3)}_{4}$. Along the same line, we arrive at three partition theorems which may be regarded as an $A^{(2)}_{4}$ analog of the
Externí odkaz:
http://arxiv.org/abs/2211.12351
Autor:
Tsuchioka, Shunsuke
We define a length function for a perfect crystal. As an application, we derive a variant of the Rogers-Ramanujan identities which involves (a $q$-analog of) the Fibonacci numbers.
Comment: This is an early draft for a talk for the conference "R
Comment: This is an early draft for a talk for the conference "R
Externí odkaz:
http://arxiv.org/abs/2211.04296
Autor:
Tsuchioka, Shunsuke
We give another proof of the second Rogers-Ramanujan identity by Kashiwara crystals.
Comment: 6 pages, a submitted version
Comment: 6 pages, a submitted version
Externí odkaz:
http://arxiv.org/abs/2205.06038
Autor:
Tsuchioka, Shunsuke
We give manifestly positive Andrews-Gordon type series for the level 3 standard modules of the affine Lie algebra of type $A^{(1)}_2$. We also give corresponding bipartition identities which have representation theoretic interpretations via the verte
Externí odkaz:
http://arxiv.org/abs/2205.04811
Autor:
Takigiku, Motoki, Tsuchioka, Shunsuke
We give Andrews-Gordon type series for the principal characters of the level 5 and 7 standard modules of the affine Lie algebra $A^{(2)}_{2}$. We also give conjectural series for some level 2 modules of $A^{(2)}_{13}$.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/2006.02630
Autor:
Takigiku, Motoki, Tsuchioka, Shunsuke
We generalize the theory of linked partition ideals due to Andrews using finite automata in formal language theory and apply it to prove three Rogers--Ramanujan type identities of modulo 14 that were posed by Nandi through vertex operator theoretic c
Externí odkaz:
http://arxiv.org/abs/1910.12461
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Autor:
Tsuchioka, Shunsuke
Stembridge characterized regular crystals associated with a simply-laced generalized Cartan matrix (GCM) in terms of local graph-theoretic quantities. We give a similar axiomatization for $B_2$ regular crystals and thus for regular crystals associate
Externí odkaz:
http://arxiv.org/abs/1710.09622
Autor:
Tsuchioka, Shunsuke
We verify the Brou\'e-Malle-Rouquier (BMR) freeness for cyclotomic Hecke algebras associated with complex reflection groups $G_{17}$, $G_{18}$, $G_{19}$ in the Shephard-Todd classification. Together with results of Ariki, Ariki-Koike, Brou\'e-Malle,
Externí odkaz:
http://arxiv.org/abs/1710.03868