scholarly journals Exact spectrum of the XXZ open spin chain from theq-Onsager algebra representation theory

2007 ◽  
Vol 2007 (09) ◽  
pp. P09006-P09006 ◽  
Author(s):  
Pascal Baseilhac ◽  
Kozo Koizumi
Keyword(s):  
Representation Theory ◽  
Spin Chain ◽  
Algebra Representation ◽  
Onsager Algebra

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 QUANTUM AFFINE SYMMETRY IN VERTEX MODELS

1993 ◽  
Vol 08 (08) ◽  
pp. 1479-1511 ◽  
Author(s):  
MAKOTO IDZUMI ◽  
TETSUJI TOKIHIRO ◽  
KENJI IOHARA ◽  
MICHIO JIMBO ◽  
TETSUJI MIWA ◽  
...  
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Spin Chain ◽  
Vertex Model ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Affine Symmetry ◽  
Higher Spin ◽  
Local Operators ◽  
The One

We study the higher spin analogs of the six-vertex model on the basis of its symmetry under the quantum affine algebra [Formula: see text]. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer matrix, vacuum, creation/ annihilation operators of particles, and local operators, purely in the language of representation theory. We find that, regardless of the level of the representation involved, the particles have spin 1/2, and that the n-particle space has an RSOS type structure rather than a simple tensor product of the one-particle space. This agrees with the picture proposed earlier by Reshetikhin.

WB algebra representation theory

1990 ◽  
Vol 339 (1) ◽  
pp. 177-190 ◽  
Author(s):  
G.M.T. Watts
Keyword(s):  
Representation Theory ◽  
Algebra Representation

scholarly journals On the representation theory of the infinite Temperley–Lieb algebra

2020 ◽  
pp. 2150205
Author(s):  
Stephen T. Moore
Keyword(s):  
Representation Theory ◽  
Spin Chain ◽  
Link State ◽  
Indecomposable Representations ◽  
Finite Dimensional ◽  
Weyl Duality

We begin the study of the representation theory of the infinite Temperley–Lieb algebra. We fully classify its finite-dimensional representations, then introduce infinite link state representations and classify when they are irreducible or indecomposable. We also define a construction of projective indecomposable representations for TL[Formula: see text] that generalizes to give extensions of TL[Formula: see text] representations. Finally, we define a generalization of the spin chain representation and conjecture a generalization of Schur–Weyl duality.

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.

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