Super boson-fermion correspondence

Victor G. Kac; J. W. Van de Leur

Displaying similar documents to “Super boson-fermion correspondence”

Generalized Verma modules, loop space cohomology and MacDonald-type identities

J. Lepowsky (1979)

Annales scientifiques de l'École Normale Supérieure

Similarity:

$ℤ$ -graded Lie superalgebras of infinite depth and finite growth

Nicoletta Cantarini (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

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.

Decomposing oscillator representations of $𝔬𝔰𝔭 (2 n / n; ℝ)$ by a super dual pair $𝔬𝔰𝔭 (2 / 1; ℝ) \times 𝔰𝔬 {(n)}^{*}$

Kyo Nishiyama (1991)

Compositio Mathematica

Similarity:

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

Similarity:

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 $G \neq ℙ (m), S ℙ (m)$ 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

Similarity:

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...

Displaying similar documents to “Super boson-fermion correspondence”

Generalized Verma modules, loop space cohomology and MacDonald-type identities

ℤ -graded Lie superalgebras of infinite depth and finite growth

Decomposing oscillator representations of 𝔬𝔰𝔭 ( 2 n / n ; ℝ ) by a super dual pair 𝔬𝔰𝔭 ( 2 / 1 ; ℝ ) × 𝔰𝔬 ( n ) *

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

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

$ℤ$ -graded Lie superalgebras of infinite depth and finite growth

Decomposing oscillator representations of $𝔬𝔰𝔭 (2 n / n; ℝ)$ by a super dual pair $𝔬𝔰𝔭 (2 / 1; ℝ) \times 𝔰𝔬 {(n)}^{*}$

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

Representations of $s l_{q} (3)$ at the roots of unity