Semi-infinite highest weight categories

Abstract

We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either upper finite or lower finite. We also consider various more general sorts of stratified categories. In the upper finite cases, we give an alternative characterization of these categories in terms of based quasi-hereditary algebras and based stratified algebras, which are certain locally unital algebras possessing triangular bases.

Final version, accepted for publication in Memoirs AMS

References in corpus (7)

• Affine highest weight categories and affine quasihereditary algebras
• Modular representation theory in type A via Soergel bimodules
• Monoidal abelian envelopes
• Representations of the oriented skein category
• The representation theory of Brauer categories I: triangular categories
• Heisenberg and Kac-Moody categorification
• The primitive spectrum and category O for the periplectic Lie superalgebra

Cited by in corpus (14)

• Whittaker modules for classical Lie superalgebras
• Tilting modules for classical Lie superalgebras
• The representation theory of Brauer categories I: triangular categories
• Quivers for SL(2) tilting modules
• The classification of blocks in BGG category O
• Parabolic category ${\mathcal{O}}^{\mathfrak{p}}$ for periplectic Lie superalgebras $\mathfrak{pe}(n)$
• Cellularity of endomorphism algebras of tilting objects
• Blocks and characters of $G(3)$-modules of non-integral weights
• Representations of weakly triangular categories
• The $q$-Schur category and polynomial tilting modules for quantum $G{L}_n$
• Representation theory of a semisimple extension of the Takiff superalgebra
• Graded triangular bases
• Representations of cyclotomic oriented Brauer categories
• Khovanov algebras for the periplectic Lie superalgebras