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Abstract

We investigate a generalization of the classical notion of a Schur functor associated to a ribbon diagram. These functors are defined with respect to an arbitrary algebra, and in the case that the underlying algebra is the symmetric/exterior algebra, we recover the classical definition of Schur/Weyl functors, respectively. In general, we construct a family of 3-term complexes categorifying the classical concatenation/nearconcatenation identity for symmetric functions, and one of our main results is that the exactness of these 3-term complexes is equivalent to the Koszul property of the underlying algebra A. We further generalize these ribbon Schur functors to the notion of a multi-Schur functor and construct a canonical filtration of these objects whose associated graded pieces are described explicitly; one consequence of this filtration is a complete equivariant description of the syzygies of arbitrary Segre products of Koszul modules over the Segre product of Koszul algebras.

Document Type

Article

Publication Date

1-1-2025

Notes/Citation Information

Publisher Copyright: © 2025 MSP (Mathematical Sciences Publishers).

Digital Object Identifier (DOI)

10.2140/ant.2025.19.771

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