Related papers: Superopers revisited
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require…
We consider a problem which may be viewed as an inverse one to the Schwinger realization of Lie algebra, and suggest a procedure of deforming the so-obtained algebra. We illustrate the method through a few simple examples extending…
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the…
We investigate various spaces of $SL(r+1)$-opers and their deformations. For each type of such opers, we study the quantum/classical duality, which relates quantum integrable spin chains with classical solvable many body systems. In this…
Level-one representations of the quantum affine superalgebra $U_q[\hat{gl(N|N)}]$ associated to the appropriate non-standard system of simple roots and $q$-vertex operators (intertwining operators) associated with the level-one modules are…
Notions of quasi-classical Lie-super algebra as well as Lie-super triple systems have been given and studied with some examples. Its application to Yang-Baxter equation has also been given.
In this paper, the notion of unitary vertex operator superalgebra is introduced. It is proved that the vertex operator superalgebras associated to the unitary highest weight representations for the Neveu-Schwarz Lie superalgebra, Heisenberg…
Higher structures - infinity algebras and other objects up to homotopy, categorified algebras, `oidified' concepts, operads, higher categories, higher Lie theory, higher gauge theory... - are currently intensively investigated in…
The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a…
We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasi-Yang-Baxter algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and…
The quasi-Gaudin algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation of the quasi-Gaudin algebra, we obtain a class of bosonic models which exhibit this curious…
We build in this paper the algebra of q-deformed pseudo-differential operators shown to be an essential step towards setting a q-deformed integrability program. In fact, using the results of this q-deformed algebra, we derive the…
We review the Euclidean Hopf algebra $U_q(e^N)$ dual of $Fun(\rn_q^N\lcross SO_{q^{-1}}(N))$ and describe its fundamental Hilbert space representations \cite{fioeu}, which turn out to be rather simple "lattice-regularized" versions of the…
We discuss quiver gauge models with matter fields based on Dynkin diagrams of Lie superalgebra structures. We focus on A(1,0) case and we find first that it can be related to intersecting complex cycles with genus $g$. Using toric geometry,…
In this article, we give Maurer-Cartan characterizations of equivariant Lie superalgebra structures. We introduce equivariant cohomology and equivariant formal deformation theory of Lie superalgebras. As an application of equivariant…
It is known that the operads of perm algebras and pre-Lie algebras are the Koszul dual each other and hence there is a Lie algebra structure on the tensor product of a perm algebra and a pre-Lie algebra. Conversely, we construct a special…
Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We…
Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to…
We construct quasi-solvable quantum mechanical matrix models by employing two different methods, the one is universal enveloping algebra of Lie superalgebra and the other is N-fold supersymmetry. For the former we examine the q(2) and…
We examine the Onsager algebra symmetry of $\tau^{(j)}$-matrices in the superintegrable chiral Potts model. The comparison of Onsager algebra symmetry of the chiral Potts model with the $sl_2$-loop algebra symmetry of six-vertex model at…