발표는 온라인으로 진행됩니다. This talk will be online only (via Zoom)

Meeting address : 845 9952 4320 (no password)

or Zoom link : https://snu-ac-kr.zoom.us/j/84599524320

Abstract : Let g be a Lie superalgebra and f be an even nilpotent in g. This talk introduces two approaches for constructing the classical W-superalgebra structure W(g, f) by explicitly calculating their generators and Poisson λ-brackets. The first approach is to reinterpret the bracket relations among the generators of classical W-superalgebras, given a basis of the centralizer g^f. To achieve this, we introduce Dirac reductions of Poisson vertex superalgebras. A modified Dirac reduction is then employed to realize Poisson λ-brackets in classical W-superalgebras within the affine Poisson vertex superalgebra. We repeat the analogous arguments to reinterpret Poisson λ-brackets of classical SUSY W-algebras W(g, F) as the Dirac reduced brackets. The second approach is constructing integrable systems on classical W-superalgebras W(g, f), where f is an even rectangular nilpotent element in g := gl_{m|n}. To this end, we introduce super Adler-type operators inspired by the super-analogue of Gelfand-Dickey algebras. We demonstrate their role in obtaining Poisson vertex superalgebras isomorphic to W(g, f) since being a super Adler-type is preserved by taking quasi-determinants of matrix-valued pseudo-differential operators. Using the Lenard-Magri scheme, we prove the existence of integrable hierarchies on these rectangular W-superalgebras.