Related papers: Decomposing Nekrasov Decomposition
We generalize our analysis in [arXiv:1301.1977], and show that a 5d and 6d AGT correspondence for SU(N) -- which essentially relates the relevant 5d and 6d Nekrasov instanton partition functions to the integrable representations of a…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
We relate various approaches to coefficient systems in relative integral $p$-adic Hodge theory, working in the geometric context over the ring of integers of a perfectoid field. These include small generalised representations over…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
We define several "standard" subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show…
We investigate the representation theory of the rational and trigonometric Cherednik algebra of type $GL_n$ by means of combinatorics on periodic (or cylindrical) skew diagrams. We introduce and study standard tableaux and plane partitions…
Let $(X,\omega)$ be a symplectic orbifold which is locally like the quotient of a $\mathbb{Z}_2$ action on $\reals^n$. Let $A^{((\hbar))}_X$ be a deformation quantization of $X$ constructed via the standard Fedosov method with…
We obtain some simple relations between decomposition numbers of quantized Schur algebras at an n-th root of unity (over a field of characteristic 0). These relations imply that every decomposition number for such an algebra occurs as a…
A tuple of commuting operators $(S_1,\dots,S_{n-1},P)$ for which the closed symmetrized polydisc $\Gamma_n$ is a spectral set is called a $\Gamma_n$-contraction. We show that every $\Gamma_n$-contraction admits a decomposition into a…
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…
Higher-point correlation functions encode the data of infinitely many 4-point correlators in conformal field theory (CFT). In this paper, we develop new tools to efficiently extract this data from multi-point crossing equations. Concretely,…
We establish a genericity property in the representation theory of a flat family of finite-dimensional algebras in the sense of Cline-Parshal-Scott. More precisely, we show that the decomposition matrices as introduced by Geck and Rouquier…
Conformal blocks of Liouville theory have a Coulomb-gas representation as Dotsenko-Fateev (DF) integrals over the positions of screening charges. For q-deformed Liouville, the conformal blocks on a sphere with an arbitrary number of…
An extension of the AGT relation from two to three dimensions begins from connecting the theory on domain wall between some two S-dual SYM models with the 3d Chern-Simons theory. The simplest kind of such a relation would presumably connect…
The aim of this paper is to review our results on description of the multi-parameter deformed oscillators and their oscillator algebras. We define generalized (q;\alpha,\beta,\gamma;\nu)-deformed oscillator algebra and study its irreducible…
We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include…
The quantum toroidal algebra of $gl_1$ provides many deformed W-algebras associated with (super) Lie algebras of type A. The recent work by Gaiotto and Rapcak suggests that a wider class of deformed W-algebras including non-principal cases…
We give an explicit combinatorial description of the deformation theory of the Abelian category of (quasi)coherent sheaves on any separated Noetherian scheme $X$ via the deformation theory of path algebras of quivers with relations, by…
This paper presents a method for constructing flat deformations of associative algebras. We will refer to this method as method two because it is a generalisation of the method obtained in [1]. The deformations obtained using the first two…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…