Tensor products of the defining representations over the Witt algebra in positive characteristic

2021/08/15 by Hao Chang, Yu-Feng Yao, Chang, Hao +1
Mathematics · #17B10 #17B50 #17B70 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B10 #msc:17B50 #msc:17B70

paper · pdf · doi:10.48550/arxiv.2108.06657

11 pages

arxiv created 2021/08/15 · openalex publication_date 2021/08/15 · arxiv updated 2021/08/17 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28

Abstract

Let A(1):=k[X]/(X^p) be the natural representation of the Witt algebra W(1) over an algebraically closed field of prime characteristic p>3. In this note, we decompose the W(1)-module A(1)⊗ A(1) into two invariant subspaces, and precisely construct their Jordan-Hölder composition series. As a consequence, we obtain all decomposition factors of the tensor product of the simple restricted W(1)-module with "highest" weight p-1.

Related

• Simple weight modules with finite-dimensional weight spaces over Witt superalgebras
• 1-cocycles of the Witt algebra with coefficients in tensor product of modules
• Tensor modules over Witt superalgebras
• Extensions of simple modules for the Witt algebra
• Ext¹-quivers for the Witt algebra W(1,1)