Fully commutative elements and spherical nilpotent orbits
| Autor: | Jacopo Gandini |
|---|---|
| Přispěvatelé: | Gandini, Jacopo |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Mathematics::Rings and Algebras abelian ideals of Borel subalgebras Mathematics - Algebraic Geometry fully commutative element FOS: Mathematics nilpotent orbit Mathematics - Combinatorics 17B08 20F55 Combinatorics (math.CO) Representation Theory (math.RT) Mathematics::Representation Theory Algebraic Geometry (math.AG) Mathematics - Representation Theory |
| Popis: | Let g be a simple Lie algebra, with fixed Borel subalgebra b and with Weyl group W. Expanding on previous work of Fan and Stembridge in the simply laced case, this note aims to study the fully commutative elements of W, and their connections with the spherical nilpotent orbits in g. If g is not of type G_2, it is shown that an element w in W is fully commutative if and only if the subalgebra of b determined by the inversions of w lies in the closure of a spherical nilpotent orbit. A similar characterization is also given for the ad-nilpotent ideals of b, which are parametrized by suitable elements in the affine Weyl group of g thanks to the work of Cellini and Papi. v3: final version, to appear on Journal of Algebra |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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