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The incidence Hopf algebra of graphs
combinatorial Hopf algebra graph chromatic polynomial
2011/2/24
The graph algebra is a commutative, cocommutative, graded,connected incidence Hopf algebra, whose basis elements correspond to fi-nite simple graphs and whose Hopf product and coproduct admit simple c...
A note on the $O_q(\hat{sl_2})$ algebra
Current algebra q− Onsager algebra Quantum integrable models
2011/2/25
An explicit homomorphism that relates the elements of the infinite dimensional non-Abelian
algebra generating Oq(csl2) currents and the standard generators of the q−Onsager algebra is proposed....
Geometric approach to Hall algebra of representations of Quivers over local ring
Quantum generalized Kac-Moody algebra Hall algebra quiver local ring
2011/2/25
The category of representations of a Dynkin quiver over local ring R = k[t]/(tn) is not hereditary any more. The Hall algebra defined on this category doesn’t have a well defined coalgebraic structure...
Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model
Quantized Nambu-Poisson Manifolds 3-Lie Algebra Reduced Model
2011/3/2
We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to a zero-dimensional 3-Lie algebra model and construct various stable solutions corresponding to quantized Nambu-Poisson mani...
Algebra of differential operators associated with Young diagrams
Algebra of differential operators Young diagrams
2011/1/17
We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to the algebra of the co...
Higher Lie algebra actions on Lie algebroids
Lie algebroid NQ-manifold double Lie algebroid higher Lie algebra action
2011/1/17
We consider a simple instance of action up to homotopy. More precisely, we consider non-strict actions of DGLAs in degrees −1 and 0 on degree 1 NQ-manifolds. In a more conventional language this...
Finite-dimensional vertex algebra modules over fixed point commutative subalgebras
vertex algebra Galois extension commutative algebra
2011/1/18
Let A be a connected commutative C-algebra with derivation D,G a finite linear automorphism group of A which preserves D, and R = AG the fixed point subalgebra of A under the action of G. We show that...
The GL_n(q)-module structure of the symmetric algebra around the Steinberg module
GL_n(q)-module structure symmetric algebra Steinberg module
2011/1/17
We determine the graded composition multiplicity in the symmetric algebra S•(V ) of the natural GLn(q)-module V , or equivalently in the coinvariant algebra of V ,for a large class of irreducibl...
Intertwining operators for Sklyanin algebra and elliptic hypergeometric series
operators for Sklyanin algebra elliptic hypergeometric series
2010/12/28
Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ℓ and −ℓ − 1 are constructed using the technique of intertwin-ing vectors for...
Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end
Dynamical reflection algebra Boundary SOS model Factorizing Drinfel’d twist
2010/12/28
We introduce in this paper an elliptic dynamical reflection algebra describing an SOS model with reflecting end. Using factorizing Drinfel’d twist, we compute the partition function of this model with...
Pentagonal Relations and the Exchange Module of the Type $A_n$ Cluster Algebra
Associahedron Cluster Algebra Discrete Homotopy Theory
2011/1/21
In this paper we study relations between the exchange relations in the cluster algebra of type-An, which has the 1-skeleton of the associahedron as its exchange graph, and the complex of triangulation...
Iterative character constructions for algebra groups
Iterative character constructions algebra groups
2011/1/20
We construct a family of orthogonal characters of an algebra group which decompose the supercharacters defined by Diaconis and Isaacs [6]. Like supercharacters, these characters are
given by nonnegat...
A Boolean algebra and a Banach space obtained by push-out iteration
Boolean algebra Banach space push-out iteration
2011/2/25
Under the assumption that c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(!)/fin has under CH a...
Direct proofs of the Feigin-Fuchs character formula for unitary representations of the Virasoro algebra
Direct proofs of the Feigin-Fuchs character unitary representations Virasoro algebra
2011/3/1
Previously we gave a proof of the Feigin–Fuchs character formula for the irreducible unitary
discrete series of the Virasoro algebra with 0 < c < 1.
Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
Instanton partition functions N=2 SU(N) gauge theories general surface operator W-algebra duals
2011/3/2
We write down an explicit conjecture for the instanton partition functions in 4d N = 2 SU(N) gauge theories in the presence of a certain type of surface operator.