Highest weights for truncated shifted Yangians and product monomial crystals

IF 0.6 2区 数学 Q3 MATHEMATICS
J. Kamnitzer, P. Tingley, Ben Webster, Alex Weekes, Oded Yacobi
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引用次数: 31

Abstract

Truncated shifted Yangians are a family of algebras which are natural quantizations of slices in the affine Grassmannian. We study the highest weight representations of these algebras. In particular, we conjecture that the possible highest weights for these algebras are described by product monomial crystals, certain natural subcrystals of Nakajima's monomials. We prove this conjecture in type A. We also place our results in the context of symplectic duality and prove a conjecture of Hikita in this situation.
截断移位洋晶体和乘积单晶的最高重量
截移扬子是仿射格拉斯曼群中片的自然量子化代数。我们研究这些代数的最高权表示。特别地,我们推测这些代数的可能的最高权值是用乘积单项式晶体,即中岛单项式的某些自然子晶体来描述的。我们在a类型中证明了这个猜想。我们还将结果放在辛对偶的背景下,并在这种情况下证明了Hikita的一个猜想。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
9
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