A bijective proof and generalization of Siladić’s Theorem

Konan, Isaac

doi:10.1016/j.ejc.2020.103101

Cited by 5 publications

(2 citation statements)

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“…(2) 2n as a result that links the generalization of the Siladić theorem [13] for 2n primary colors to the unique level one standard module L(Λ 0 ). This fits with the original work of Siladić [19], where he stated his identity after describing a basis of the unique level one standard module of A (2) 2 through vertex operators.…”

Section: Bijection Between Ementioning

confidence: 96%

Weighted Words at Degree Two, II: Flat Partitions, Regular Partitions, and Application to Level One Perfect Crystals

Konan

2022

Electron. J. Combin.

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In a recent work, Keith and Xiong gave a refinement of Glaisher's theorem by using a Sylvester-style bijection. In this paper, we introduce two families of colored partitions, flat and regular partitions, and generalize the bijection of Keith and Xiong to these partitions. We then state two results, the first at degree one, where partitions have parts with primary colors, and the second result at degree two for secondary-colored partitions, using the result of the first paper of this series on Siladić's identity. These results allow us to easily retrieve the Frenkel-Kac character formulas of level one standard modules for the type $A _{2n}^{(2)}, D_{n+1}^{(2)}$ and B_n^{(1)}$ , and also to make the connection between the result stated in paper one and the representation theory.

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