q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations

Abstract

Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting according to Gel'fand--Tsetlin-type formulas. Unitary representations of the q-deformed algebras U_q(so_{n,1}) are found.

Latex, 5 pages; an old paper (1991) posted for archival purposes

Cited by in corpus (28)

• Coideal subalgebras in quantum affine algebras
• Universal K-matrices for quantum Kac-Moody algebras
• Coideal algebras from twisted Manin triples
• Symmetries and invariants of twisted quantum algebras and associated Poisson algebras
• Gelfand-Tsetlin bases for classical Lie algebras
• The ${\mathbb{Z}}_2^n$ Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
• Center of the universal Askey--Wilson algebra at roots of unity
• A new quantum analog of the Brauer algebra
• Classification of irreducible representations of the q-deformed algebra U'_q(so_n)
• (Quantum) twisted Yangians: symmetry, Baxterisation and centralizers
• Higher rank classical analogs of the Askey-Wilson algebra from the $s{l}_N$ Onsager algebra
• On centralizer algebras for spin representations
• Classical weight modules over $ı$quantum groups
• Dualities for spin representations
• Based modules over the $ı$quantum group of type AI
• Classification theorem on irreducible representations of the q-deformed algebra U'_q(so(n))
• Some interactions between Hopf Galois extensions and noncommutative rings
• On representations of $U_q^{\prime }s{o}_n$
• Twisted WZW Branes from Twisted REA's
• Twisted q-Yangians and Sklyanin determinants
• Boundary transfer matrices arising from quantum symmetric pairs
• Characteristic equation for symplectic groupoid and cluster algebras
• Braid group actions on coideal subalgebras of quantized enveloping algebras
• A q-analogue of the Wigner-Eckart theorem for the nonstandard q-deformed algebra U'_q(so(n))
• 2-Homogeneous bipartite distance-regular graphs and the quantum group $U_q^{\prime }({\mathfrak{so}}_6)$
• Integrable modules over quantum symmetric pair coideal subalgebras
• Generic Gelfand-Tsetlin Representations of $U_q^{\text{tw}}({\mathfrak{so}}_3)$ and $U_q^{\text{tw}}({\mathfrak{so}}_4)$
• Degenerate Series Representations of the $q$-Deformed Algebra ${\mathrm{so}}_q^{\prime }(r,s)$