For all affine Toda field theories we propose a new type of generic boundary bootstrap equations, which can be viewed as a very specific combination of elementary boundary bootstrap equations. These equations allow to construct generic solutions for the boundary reflection amplitudes, which are valid for theories related to all simple Lie algebras, that is simply laced and non-simply laced. We ...

We study the spectra of G/G coset models by computing BRST cohomology of affine Lie algebras with coefficients in tensor product of two modules. One-to-one correspondence between the spectra of A1/A 1 1 and that of the minimal matter coupled to gravity (including boundary states of the Kac table) is observed. This phenomena is discussed from the point of hamiltonian reduction of BRST complexes ...

Starting from Borcherds’ fake monster Lie algebra we construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for...

We study the structure of Yangians of affine type and deformed double current algebras, which are deformations of the enveloping algebras of matrix W1+∞-algebras. We prove that they admit a PBWtype basis, establish a connection (limit construction) between these two types of algebras and toroidal quantum algebras, and we give three equivalent definitions of deformed double current algebras. We ...

The object of this work is the systematical study of a certain type of generalized Cartan matrices associated with the Dynkin diagrams that characterize CartanLie and affine Kac-Moody algebras. These generalized matrices are associated to graphs which arise in the study and classification of Calabi-Yau spaces through Toric Geometry. We focus in the study of what should be considered the general...

We classify irreducible Whittaker modules for generalized Heisenberg Lie algebra t and irreducible Whittaker modules for Lie algebra t̃ obtained by adjoining m degree derivations d1, d2, . . . , dm to t. Using these results, we construct imaginary Whittaker modules for non-twisted extended affine Lie algebras and prove that the imaginary Whittaker modules of Z-independent level are always irredu...

We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie algebras. One is defined via combinatorial properties and is easy to calculate; the other is closely related to the q = 1 limit of the “minimal affinization” rep...

We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. introduce twisted cartesian product two algebras according to linear representations by infinitesimal transformations. also exhibit double extension process algebra which allows us get all simply connected groups with bi-invariant symplectic connections. All constructed performin...

Picard groups of tensor categories play an important role in rational conformal field theory. The Picard group of the representation category C of a rational vertex algebra can be used to construct examples of (symmetric special) Frobenius algebras in C. Such an algebra A encodes all data needed to ensure the existence of correlators of a local conformal field theory. The Picard group of the ca...