The Kostant form of \mathfrakU(sl_n⁺) and the Borel subalgebra of the Schur algebra S(n,r)

2008/03/31 by Ana Paula Santana, Santana, Ana Paula, Ivan Yudin +1 · 1 citation
Mathematics · #16E05 #16E60 #16G99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0803.4382

openalex publication_date 2008/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A_n(K) be the Kostant form of \mathfrakU(sl_n⁺) and Γ the monoid generated by the positive roots of sl_n. For each λ∈ Λ(n,r) we construct a functor F_λ from the category of finitely generated Γ-graded A_n(K)-modules to the category of finite dimensional S⁺(n,r)-modules, with the property that F_λ maps (minimal) projective resolutions of the one-dimensional A_n(K)-module K_A to (minimal) projective resolutions of the simple S⁺(n,r)-module K_λ.

Citations

• Minimal Resolutions of Algebras

Cited by

• Gröbner basis and Anick's resolution for U_F2(sl⁺₃)

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• Kostant modules in blocks of category \mathcal O_S
• Combinatorial and geometric constructions associated with the Kostant cascade
• Presenting Schur algebras as quotients of the universal enveloping algebra of gl(2)
• Resolutions over Koszul algebras
• Resolutions of standard modules over KLR algebras of type A