Seminario del 2023
22/05/2023
26/05/2023
26/05/2023
Martina Lanini
Relazione all'interno del convegno: Quiver Representations, Quiver Varieties and Combinatorics
Symmetric quivers and symmetric varieties
In this talk I will report on ongoing joint work with Ryan
Kinser and Jenna Rajchgot on varieties of symmetric quiver
representations. These varieties are acted upon by a reductive group via
change of basis, and it is natural to ask for a parametrisation of the
orbits, for the closure inclusion relation among them, for information
about the singularities arising in orbit closures. Since the Eigthies,
same (and further) questions about representation varieties for type A
quivers have been attached by relating such varieties to Schubert
varieties in type A flag varieties (Zelevinsky, Bobinski-Zwara, ...). I
will explain that in the symmetric setting it is possible to interpret
the above questions in terms of certain symmetric varieties. More
precisely, we show that singularities of an orbit closure of a symmetric
quiver representation variety are smoothly equivalent to singularities
of an appropriate Borel orbit closure in a symmetric variety.