Related papers: Bethe Algebra using Pure Spinors

A new approach to polarization algebra is introduced. It exploits the geometric properties of spinors in order to represent wave states consistently in arbitrary directions in three dimensional space. In this first expository paper of an…

The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…

We present a method for introducing and analysing higher-derivative deformations of maximally supersymmetric field theories. Such terms are built in the pure spinor superfield framework, using a set of operators representing physical…

We consider the action of the Bethe algebra B_K on (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda, the weight subspace of weight $\lambda$ of the tensor product of k polynomial irreducible gl_N-modules with highest weights…

In this work, we propose a novel framework for defining the dual structure of a spinor. This construction relies on the basis elements of the Clifford algebra, leading to a covariant structure that embeds the dual. The formulation includes…

For any row-finite graph $E$ and any field $K$ we construct the {\its Leavitt path algebra} $L(E)$ having coefficients in $K$. When $K$ is the field of complex numbers, then $L(E)$ is the algebraic analog of the Cuntz Krieger algebra…

We show the equivalence of the different types of pure spinor constraints geometrically derived from the Free Differential Algebras of N=2 d=10 supergravities. Firstly, we compute the general solutions of these constraints, using both a G_2…

We consider Borcherds superalgebras obtained from semisimple finite-dimensional Lie algebras by adding an odd null root to the simple roots. The additional Serre relations can be expressed in a covariant way. The spectrum of generators at…

We give a simple algebraic model for rational G-spectra over an exceptional subgroup, for any compact Lie group G. Moreover, all our Quillen equivalences are symmetric monoidal, so as a corollary we obtain a monoidal algebraic model for…

Based on the inhomogeneous T-Q relation and the associated Bethe Ansatz equations obtained via the off-diagonal Bethe Ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries…

We prove that for any k greater or equal to 2, given a smooth compact k-dimensional manifold and a multiplicative k-1-gerbe on a Lie group, together with an integrable connection, there is a line bundle on the corresponding…

We present in an unified and detailed way the Nested Bethe Ansatz for closed spin chains based on Y(gl(n)), Y(gl(m|n)), U_q(gl(n)) or U_q(gl(m|n)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain. In…

Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial…

The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator…

We present two new integrable spin ladder models which posses three general free parameters besides the rung coupling J. Wang's systems based on the SU(4) and SU(3/1) symmetries can be obtained as special cases. The models are exactly…

For a field K and directed graph E, we analyze those elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E), L_K(E)]. This analysis allows us to give easily computable necessary and sufficient conditions to…

We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin,…

In this note we report the results of our study of a 1D integrable spin chain whose critical behaviour is governed by a CFT possessing a continuous spectrum of scaling dimensions. It is argued that the computation of the density of Bethe…

Let G be any of the complex classical groups GL(n), SO(2n+1), Sp(2n), O(2n), let g denote the Lie algebra of G, and let Z(g) denote the subalgebra of G-invariants in the universal enveloping algebra U(g). We derive a Taylor-type expansion…