Gelfand–Tsetlin bases for classical Lie algebras
AI Molev - Handbook of algebra, 2006 - Elsevier
The theory of semisimple Lie algebras and their representations lies in the heart of modern
mathematics. It has numerous connections with other areas of mathematics and physics …
mathematics. It has numerous connections with other areas of mathematics and physics …
Representations of quantum affine superalgebras
H Zhang - Mathematische Zeitschrift, 2014 - Springer
We study the quantum affine superalgebra U_q (L sl (M, N)) U q (L sl (M, N)) and its finite-
dimensional representations. We prove a triangular decomposition and establish a system …
dimensional representations. We prove a triangular decomposition and establish a system …
Structure and representations of the quantum general linear supergroup
RB Zhang - Communications in mathematical physics, 1998 - Springer
The structure and representations of the quantum general linear supergroup GL q (m| n) are
studied systematically by investigating the Hopf superalgebra G q of its representative …
studied systematically by investigating the Hopf superalgebra G q of its representative …
Gelfand-Tzetlin coordinates for the unitary supergroup
T Guhr - Communications in mathematical physics, 1996 - Springer
Abstract The Gelfand-Tzetlin method provides explicit coordinates on the parameter space
of the unitary group U (k) which make direct evaluations of group integrals possible. It is …
of the unitary group U (k) which make direct evaluations of group integrals possible. It is …
Gelfand–Tsetlin bases of representations for super Yangian and quantum affine superalgebra
K Lu - Letters in Mathematical Physics, 2021 - Springer
We give explicit actions of Drinfeld generators on Gelfand–Tsetlin bases of super Yangian
modules associated with skew Young diagrams. In particular, we give another proof that …
modules associated with skew Young diagrams. In particular, we give another proof that …
Gel'fand–Zetlin basis and Clebsch–Gordan coefficients for covariant representations of the Lie superalgebra gl (m∣ n)
NI Stoilova, J Van der Jeugt - Journal of mathematical physics, 2010 - pubs.aip.org
A Gel'fand–Zetlin basis is introduced for the irreducible covariant tensor representations of
the Lie superalgebra gl (m∣ n). Explicit expressions for the generators of the Lie …
the Lie superalgebra gl (m∣ n). Explicit expressions for the generators of the Lie …
Classical and quantum sl(1‖2) superalgebras, Casimir operators and quantum chain Hamiltonians
D Arnaudon, C Chryssomalakos… - Journal of Mathematical …, 1995 - pubs.aip.org
We examine in this paper the two parameter deformed superalgebra 𝒰 qs (sl (1‖ 2)) and
use the results in the construction of quantum chain Hamiltonians. This study is done both in …
use the results in the construction of quantum chain Hamiltonians. This study is done both in …
Centre and representations of at roots of unity
B Abdesselam, D Arnaudon… - Journal of Physics A …, 1997 - iopscience.iop.org
Quantum groups at the roots of unity have the property that their centre is enlarged.
Polynomial equations relate the standard deformed Casimir operators and the new central …
Polynomial equations relate the standard deformed Casimir operators and the new central …
Finite‐dimensional representations of the quantum superalgebra Uq[gl(2/2)]. II. Nontypical representations at generic q
NA Ky, NI Stoilova - Journal of Mathematical Physics, 1995 - pubs.aip.org
The construction approach proposed in the previous paper [NA Ky, J. Math. Phys. 35, 2583
(1994)] allows us there and in the present paper to construct at generic deformation …
(1994)] allows us there and in the present paper to construct at generic deformation …
Infinitely many two-variable generalisations of the Alexander–Conway polynomial
D De Wit, A Ishii, J Links - Algebraic & Geometric Topology, 2005 - msp.org
We show that the Alexander-Conway polynomial Δ is obtainable via a particular one-
variable reduction of each two-variable Links–Gould invariant LG m, 1, where m is a positive …
variable reduction of each two-variable Links–Gould invariant LG m, 1, where m is a positive …