Semi-infinite combinatorics in representation theory
Martina Lanini
TL;DR
This paper explores semi-infinite combinatorics within representation theory, proposing a semi-infinite moment graph theory and demonstrating how to compute local intersection cohomology stalks using an existing algorithm.
Contribution
It introduces a semi-infinite moment graph framework and connects it to the geometric aspects of semi-infinite flag varieties, advancing computational methods in the field.
Findings
Computed stalks of local intersection cohomology of semi-infinite flag varieties.
Linked semi-infinite combinatorics to geometric representation theory.
Proposed a new semi-infinite moment graph theory.
Abstract
In this work we discuss some appearances of semi-infinite combinatorics in representation theory. We propose a semi-infinite moment graph theory and we motivate it by considering the (not yet rigorously defined) geometric side of the story. We show that it is possible to compute stalks of the local intersection cohomology of the semi-infinite flag variety, and hence of spaces of quasi maps, by performing an algorithm due to Braden and MacPherson.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology