Some branching formulas for Kac--Moody Lie algebras

Jerzy Weyman; Kyu-Hwan Lee

Some branching formulas for Kac--Moody Lie algebras

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arxiv 1804.10251 v3 pith:XKQ5F363 submitted 2018-04-26 math.RT math.ACmath.RA

Kyu-Hwan Lee , Jerzy Weyman This is my paper · ORCID

classification math.RTmath.ACmath.RA

keywords somealgebrasbranchingformulasgenerickac--moodyringsassociated

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abstract

In this paper we give some branching rules for the fundamental representations of Kac--Moody Lie algebras associated to $T$-shaped graphs. These formulas are useful to describe generators of the generic rings for free resolutions of length three described in [JWm16]. We also make some conjectures about the generic rings.

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Residual Intersections and Schubert Varieties
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For ADE types with an extremal or minuscule vertex, each opposite Schubert variety on one arm of the graph G_k has defining ideal given by a residual intersection of the linked variety on the other arm.

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