Marco Trevisiol (Sapienza Università di Roma)

Normality of Closures of Orthogonal Nilpotent Symmetric Orbits

  • Data: 07 GIUGNO 2022  dalle 15:00 alle 16:00

  • Luogo: Seminario 1 ore 15.00

Kraft and Procesi showed that the Zariski closure of the conjugacy classes of type A are all normal and, in type B, C and D, they have described which ones are normal. In their work the Lie group acts on its Lie algebra by the adjoint action. In types B, C, D, a similar question can be asked for the action of the Lie group on the odd part of the general linear Lie algebra; that is the orthogonal group acting on the symmetric matrices and the symplectic group acting on the symmetric-symplectic matrices. Ohta showed that in the latter case every orbit has normal closures while this conclusion is not valid in the former case. In this talk I will present the main result of my Ph.D. thesis which gives a combinatorial description of the orbit whose closures are normal in the orthogonal case.