Displaying similar documents to “Super boson-fermion correspondence”

ℤ -graded Lie superalgebras of infinite depth and finite growth

Nicoletta Cantarini (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In 1998 Victor Kac classified infinite-dimensional ℤ -graded Lie superalgebras of finite depth. We construct new examples of infinite-dimensional Lie superalgebras with a ℤ -gradation of infinite depth and finite growth and classify ℤ -graded Lie superalgebras of infinite depth and finite growth under suitable hypotheses.

Cohomology of G / P for classical complex Lie supergroups G and characters of some atypical G -modules

Ivan Penkov, Vera Serganova (1989)

Annales de l'institut Fourier

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We compute the unique nonzero cohomology group of a generic G 0 - linearized locally free 𝒪 -module, where G 0 is the identity component of a complex classical Lie supergroup G and P ↪ G 0 is an arbitrary parabolic subsupergroup. In particular we prove that for G ≠ ℙ ( m ) , S ℙ ( m ) this cohomology group is an irreducible G 0 -module. As an application we generalize the character formula of typical irreducible G 0 -modules to a natural class of atypical modules arising in this way.

Representations of s ⁢ l q ⁢ 3 at the roots of unity

Nicoletta Cantarini (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper we study the irreducible finite dimensional representations of the quantized enveloping algebra U q ⁢ g associated to g = s ⁢ l ⁢ 3 , at the roots of unity. It is known that these representations are parametrized, up to isomorphisms, by the conjugacy classes of the group G = S ⁢ L ⁢ 3 . We get a complete classification of the representations corresponding to the submaximal unipotent conjugacy class and therefore a proof of the De Concini-Kac conjecture about the dimension of the U q ⁢ g -modules at the roots...