Kazhdan-Lusztig polynomials for Lie superalgebra {𝔤𝔩}(𝔪\vert𝔫)

1993 ◽  
pp. 151-166 ◽  
Author(s):  
V. Serganova
Keyword(s):  
Lie Superalgebra ◽  
Lusztig Polynomials

scholarly journals Classification of Degenerate Verma Modules for E(5, 10)

2021 ◽  
Author(s):  
Nicoletta Cantarini ◽  
Fabrizio Caselli ◽  
Victor Kac
Keyword(s):  
Infinite Number ◽  
Verma Module ◽  
Lie Superalgebra ◽  
Verma Modules ◽  
Singular Vectors ◽  
Finite Dimensional ◽  
De Rham ◽  
Via Classification

AbstractGiven a Lie superalgebra $${\mathfrak {g}}$$ g with a subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 , and a finite-dimensional irreducible $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 -module F, the induced $${\mathfrak {g}}$$ g -module $$M(F)={\mathcal {U}}({\mathfrak {g}})\otimes _{{\mathcal {U}}({\mathfrak {g}}_{\ge 0})}F$$ M ( F ) = U ( g ) ⊗ U ( g ≥ 0 ) F is called a finite Verma module. In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra $${\mathfrak {g}}=E(5,10)$$ g = E ( 5 , 10 ) with the subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 of minimal codimension. This is done via classification of all singular vectors in the modules M(F). Besides known singular vectors of degree 1,2,3,4 and 5, we discover two new singular vectors, of degrees 7 and 11. We show that the corresponding morphisms of finite Verma modules of degree 1,4,7, and 11 can be arranged in an infinite number of bilateral infinite complexes, which may be viewed as “exceptional” de Rham complexes for E(5, 10).

2-Local superderivations on the Lie superalgebra of Block type

2021 ◽  
pp. 1-16
Author(s):  
Yucai Su ◽  
Xiaoqing Yue ◽  
Xiaoyu Zhu
Keyword(s):  
Lie Superalgebra ◽  
Block Type

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

scholarly journals On the finite W-algebra for the Lie superalgebra Q(N) in the non-regular case

2017 ◽  
Vol 58 (11) ◽  
pp. 111701 ◽  
Author(s):  
Elena Poletaeva ◽  
Vera Serganova
Keyword(s):  
Lie Superalgebra ◽  
Regular Case

scholarly journals QUANTUM INTEGRABILITY OF COUPLED N=1 SUPER SINE/SINH–GORDON THEORIES AND THE LIE SUPERALGEBRA D(2,1;α)

1999 ◽  
Vol 14 (16) ◽  
pp. 2551-2580 ◽  
Author(s):  
JONATHAN M. EVANS ◽  
JENS OLE MADSEN
Keyword(s):  
Quantum Theory ◽  
Lie Superalgebra ◽  
Field Theories ◽  
Continuous Family ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Classical Level ◽  
Quantum Integrability ◽  
Integrable Quantum ◽  
Conserved Currents

We discuss certain integrable quantum field theories in 1+1 dimensions consisting of coupled sine/sinh–Gordon theories with N=1 supersymmetry, positive kinetic energy, and bosonic potentials which are bounded from below. We show that theories of this type can be constructed as Toda models based on the exceptional affine Lie superalgebra D(2,1;α)(1) (or on related algebras which can be obtained as various limits) provided one adopts appropriate reality conditions for the fields. In particular, there is a continuous family of such models in which the couplings and mass ratios all depend on the parameter α. The structure of these models is analyzed in some detail at the classical level, including the construction of conserved currents with spins up to 4. We then show that these currents generalize to the quantum theory, thus demonstrating quantum-integrability of the models.

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