scholarly journals A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra osp(m,2|2n)

Author(s):  
Sigiswald Barbier ◽  
◽  
Sam Claerebout ◽  
Hendrik De Bie ◽  
◽  
...  
2012 ◽  
Vol 19 (04) ◽  
pp. 745-754
Author(s):  
Yuezhu Wu ◽  
Xiaoqing Yue ◽  
Linsheng Zhu

In this paper, we realize Verma modules and the vector-coherent-state (VCS) representations of the orthosymplectic Lie superalgebra osp(2|2n) as differential operators with vector coefficients. We also characterize simple sub-representations of VCS representations as kernels of some finite number of differential operators. The singular vectors of the atypical representation of osp(2|2n) are explicitly given.


2016 ◽  
Vol 14 (01) ◽  
pp. 1750016
Author(s):  
Nabila El Gomdi ◽  
Rim Messaoud

We compute the first differential cohomology of the orthosymplectic Lie superalgebra [Formula: see text] with coefficients in the superspace of weighted densities [Formula: see text] on the (1, 2)-dimensional real superspace. We explicitly give 1-cocycles spanning these cohomologies. This work is the simplest generalization of a result by Basdouri and Essayari [On cohomology of the orthosymplectic superalgebra, Acta Math. Hungar. 130(1–2) (2011) 155–166].


2017 ◽  
Vol 14 (02) ◽  
pp. 1750027
Author(s):  
Hafedh Khalfoun ◽  
Thamer Faidi

Over the [Formula: see text]-dimensional supercircle [Formula: see text], we consider the action of the orthosymplectic Lie superalgebra [Formula: see text], by the Lie derivative on the superpseudodifferential operators [Formula: see text]. We compute the [Formula: see text]-relative cohomology spaces [Formula: see text], where [Formula: see text] is the affine Lie superalgebra on [Formula: see text]. We explicitly give cocycles spanning these cohomology spaces. We study the [Formula: see text]-trivial deformations of the structure of the [Formula: see text]-modules [Formula: see text].


2006 ◽  
Vol 05 (03) ◽  
pp. 307-332
Author(s):  
PIERRE-ALEXANDRE GIÉ ◽  
GEORGES PINCZON ◽  
ROSANE USHIROBIRA

Based on Kostant's cohomological interpretation of the Amitsur–Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras 𝔬𝔰𝔭(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur–Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated.


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