FEDERICO MARIA STARA

PhD Graduate

PhD program:: XXXIII


supervisor: A. De Sole
advisor: P. Papi

Thesis title: On Panyushev's Rootlets for Infinitesimal Symmetric Spaces

Let g be a simple Lie algebra, b a fixed Borel subalgebra, R the corresponding root system and W the associated Weyl group. In the first part of this work we decompose the poset of abelian ideals of b into peculiar subposets, which turn out to be isomorphic to right coset representatives obtained from specific subgroups of W. We use this to give a new proof of the Panyushev's one-to-one correspondence between maximal abelian ideals of b and long simple roots of R. In the second part of the work we extend the study to the case where g = g_0 + g_1 is a Z_2-graded Lie algebra. We study the poset of abelian subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0, and we decompose it, in the semisimple cases, into specific subposets, that we show are isomorphic to right coset representatives obtained from specific subgroups of the associated affine Weyl group.

Research products

  • 11573/1635236 - 2021 - On Panyushev's rootlets for infinitesimal symmetric spaces (07a Tesi di Dottorato)
    STARA, FEDERICO MARIA

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