Algebraic Groups Seminar

Friday, 15 March, 2024, 2.30 pm

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Venue: Ramanujan Hall

Speaker: Sulakhana Chowdhury

Affiliation: IISER Thiruvananthapuram

Host: Shripad M. Garge

Title: Permutation modules of the walled Brauer algebras

Abstract: In this talk, we will discuss the permutation modules and Young modules of the group algebras of the direct product of symmetric groups and the walled Brauer algebras. In the category of dual Specht-filtered modules, if the characteristic of the field is neither 2 nor 3, then the permutation modules are dual Specht-filtered, and the Young modules are relative projective cover of the dual Specht modules. We prove that the restrictions of the cell modules of the walled Brauer algebras to the group algebras of the direct product of the symmetric groups are dual Specht filtered, and the Young modules act as the relative projective cover of the cell modules of the walled Brauer algebras. Finally, we prove that if char K differs from 2 and 3, the permutation modules can be written as a direct sum of indecomposable Young modules.