Differential operator approach to \imathquantum groups and their oscillator representations

2022/03/08 by Zhaobing Fan, Fan, Zhaobing, Jicheng Geng +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2203.03900

openalex publication_date 2022/03/08 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

For a quasi-split Satake diagram, we define a modified q-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding \imathquantum group. In other words, we provide a differential operator approach to \imathquantum groups. Meanwhile, the oscillator representations of \imathquantum groups are obtained. The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.

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