Quantum manipulation through finite fluctuations for a generalized parametric oscillator using a lie algebra representation

2021 ◽  
Author(s):  
Ty S Beus ◽  
Jean-Francois S Van Huele ◽  
Manuel Berrondo
Keyword(s):  
Lie Algebra ◽  
Parametric Oscillator ◽  
Algebra Representation ◽  
Lie Algebra Representation

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.

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.

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

scholarly journals The Support of an Irreducible Lie Algebra Representation

1998 ◽  
Vol 209 (1) ◽  
pp. 129-142 ◽  
Author(s):  
Ivan Penkov ◽  
Vera Serganova
Keyword(s):  
Lie Algebra ◽  
Algebra Representation ◽  
Lie Algebra Representation
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