STABILITY PATTERNS IN REPRESENTATION THEORY
By Steven V. Sam, Andrew Snowden. Forum of Mathematics, Sigma, 2013
147 citations recorded by the source corpus.
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is an array of equivalences between the stable representation category and various other categories, each of which has its own flavor (representation theoretic, combinatorial, commutative algebraic, or categorical) and offers a distinct perspective on the stable category. We use this theory to produce a host of specific results: for example, the construction of injective resolutions of simple objects, duality between the orthogonal and symplectic theories, and a canonical derived auto-equivalence of the general linear theory.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3fda6a3417f604eaf28485ea7fe0aacbf07ccd4c
How researchers see this paper
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In Algebra and Number Theory
- Steven V. Sam
- Thomas Church
- Andrew Snowden
- Jordan S. Ellenberg
- Jan Draisma
- Jenny Wilson
- Rohit Nagpal
- Kiran S. Kedlaya
In Geometry and Topology
- Steven V. Sam
- Andrew Snowden
- Jordan S. Ellenberg
- Thomas Church
- Jenny Wilson
- Rohit Nagpal
- Andrew Putman
- Jan Draisma
In Mathematical Physics
- Steven V. Sam
- Andrew Snowden
- Thomas Church
- Jordan S. Ellenberg
- Andrew Putman
- Jenny Wilson
- Rohit Nagpal
- Benson Farb
Citations in the corpus
- Homology of FI-modules (2015, background): “es where every object is Noetherian. We use “Noetherian” here in the broader sense, but we acknowledge that not every FI-module is finitely generated. 1 the study of many different categories (see e.g. [SS2]), while the arguments of the present paper are quite specific to FI-modules. It would be very i”
- Gröbner methods for representations of combinatorial categories (2014, result): “ties (quite different from those in the FI case). The theory of FSop G representations, with G a symmetric group, is closely tied to the theory of ∆-modules studied in [Sn]. • The Brauer categories of [SS3], in which the objects are finite sets and the morphisms are certain Brauer diagrams. Representa”