scholarly journals On Representations of sl(n, C) Compatible with a Z2-grading

10.14311/1261 ◽  
2010 ◽  
Vol 50 (5) ◽  
Author(s):  
M. Havlíček ◽  
E. Pelantová ◽  
J. Tolar
Keyword(s):  
Irreducible Representation ◽  
Representation Theory ◽  
Lie Algebra ◽  
Finite Dimensional ◽  
Algebra Representation ◽  
Lie Algebra Representation ◽  
Generally True

This paper extends existing Lie algebra representation theory related to Lie algebra gradings. The notion of a representation compatible with a given grading is applied to finite-dimensional representations of sl(n,C) in relation to its Z2-gradings. For representation theory of sl(n,C) the Gel’fand-Tseitlin method turned out very efficient. We show that it is not generally true that every irreducible representation can be compatibly graded.

scholarly journals ON MULTI-COLOR PARTITIONS AND THE GENERALIZED ROGERS–RAMANUJAN IDENTITIES

2001 ◽  
Vol 03 (04) ◽  
pp. 533-548 ◽  
Author(s):  
NAIHUAN JING ◽  
KAILASH C. MISRA ◽  
CARLA D. SAVAGE
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Mathematical Physics ◽  
Infinite Dimensional ◽  
Algebra Representation ◽  
The Sixties ◽  
Lie Algebra Representation ◽  
New Interpretation

Basil Gordon, in the sixties, and George Andrews, in the seventies, generalized the Rogers–Ramanujan identities to higher moduli. These identities arise in many areas of mathematics and mathematical physics. One of these areas is representation theory of infinite dimensional Lie algebras, where various known interpretations of these identities have led to interesting applications. Motivated by their connections with Lie algebra representation theory, we give a new interpretation of a sum related to generalized Rogers–Ramanujan identities in terms of multi-color partitions.

Generalized Bessel Functions and Lie Algebra Representation

2005 ◽  
Vol 8 (4) ◽  
pp. 299-313 ◽  
Author(s):  
Subuhi Khan ◽  
Ghazala Yasmin
Keyword(s):  
Lie Algebra ◽  
Bessel Functions ◽  
Algebra Representation ◽  
Generalized Bessel Functions ◽  
Lie Algebra Representation

scholarly journals A combinatorial identity for the derivative of a theta series of a finite type root lattice

2003 ◽  
Vol 172 ◽  
pp. 1-30
Author(s):  
Satoshi Naito
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Finite Type ◽  
Cartan Subalgebra ◽  
Theta Series ◽  
Combinatorial Identity ◽  
Root Lattice ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Affine Lie Algebra

AbstractLet be a (not necessarily simply laced) finite-dimensional complex simple Lie algebra with the Cartan subalgebra and Q ⊂ * the root lattice. Denote by ΘQ(q) the theta series of the root lattice Q of . We prove a curious “combinatorial” identity for the derivative of ΘQ(q), i.e. for by using the representation theory of an affine Lie algebra.

scholarly journals A Minimal Representation of the Orthosymplectic Lie Supergroup

2019 ◽  
Author(s):  
Sigiswald Barbier ◽  
Jan Frahm
Keyword(s):  
Lie Algebra ◽  
Natural Generalization ◽  
Lie Superalgebras ◽  
Inner Product ◽  
Minimal Representation ◽  
Jordan Superalgebra ◽  
Algebra Representation ◽  
Sesquilinear Form ◽  
Lie Algebra Representation ◽  
Kirillov Dimension

Abstract We construct a minimal representation of the orthosymplectic Lie supergroup $OSp(p,q|2n)$ for $p+q$ even, generalizing the Schrödinger model of the minimal representation of $O(p,q)$ to the super case. The underlying Lie algebra representation is realized on functions on the minimal orbit inside the Jordan superalgebra associated with $\mathfrak{osp}(p,q|2n)$, so that our construction is in line with the orbit philosophy. Its annihilator is given by a Joseph-like ideal for $\mathfrak{osp}(p,q|2n)$, and therefore the representation is a natural generalization of a minimal representation to the context of Lie superalgebras. We also calculate its Gelfand–Kirillov dimension and construct a nondegenerate sesquilinear form for which the representation is skew-symmetric and which is the analogue of an $L^2$-inner product in the supercase.

The integrability of a Lie algebra representation

1978 ◽  
Vol 2 (5) ◽  
pp. 367-371 ◽  
Author(s):  
Jan Rusinek
Keyword(s):  
Lie Algebra ◽  
Algebra Representation ◽  
Lie Algebra Representation

scholarly journals The integration of a Lie algebra representation

1968 ◽  
Vol 26 (3) ◽  
pp. 595-600 ◽  
Author(s):  
Jacques Tits ◽  
Lucien Waelbroeck
Keyword(s):  
Lie Algebra ◽  
Algebra Representation ◽  
Lie Algebra Representation
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