2023/09/25 by Divya Setia, Setia, Divya, Tanusree Khandai +1
Mathematics · #05E10 #17B10 #17B67 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2309.14144
openalex publication_date 2023/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the structure of the finite-dimensional representations of \mathfraksl2[t], the current Lie algebra type of A1, which are obtained by taking tensor products of special Demazure modules. We show that these representations admit a Demazure flag and obtain a closed formula for the graded multiplicities of the level 2 Demazure modules in the filtration of the tensor product of two local Weyl modules for \mathfraksl2[t]. Furthermore, we derive an explicit expression for graded character of the tensor product of a local Weyl module with an irreducible \mathfraksl2[t] module. In conjunction with the results of \citeMR3210603, our findings provide evidence for the conjecture in \cite9 that the tensor product of Demazure modules of levels m and n respectively has a filtration by Demazure modules of level m + n.