Related papers: Vogel's universality and Macdonald dimensions
In this paper, we consider universal sums of generalized polygonal numbers. Fixing $m\in\mathbb{N}_{\geq 3}$, we show two finiteness theorems for universal sums of generalized polygonal numbers whose inputs have a restricted number $L$ of…
The antisymmetric square of the adjoint representation of any simple Lie algebra is equal to the sum of adjoint and $X_2$ representations. We present universal formulae for quantum dimensions of an arbitrary Cartan power of $X_2$. They are…
We combine the theory of traces in homotopical algebra with sheaf theory in derived algebraic geometry to deduce general fixed point and character formulas. The formalism of dimension (or Hochschild homology) of a dualizable object in the…
We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such solution, whose expression is quite compact and simple, greatly simplifies the study of theories…
Rowland found a matrix product formula for generating functions counting binomial coefficients by their $p$-adic valuations. A natural generalization of binomial coefficients was introduced by Knuth and Wilf defined by a sequence $C$. We…
Chern-Simons models for gravity are interesting because they provide with a truly gauge-invariant action principle in the fiber-bundle sense. So far, their main drawback has largely been the perceived remoteness from standard General…
A theory of degenerate metrics is developed and applied to the problem of unifying gravitation with electromagnetism. The approach is similar to the Kaluza-Klein approach with a fifth dimension, however no ad hoc conditions are needed to…
We present an explicit difference operator diagonalized by the Macdonald polynomials associated with an (arbitrary) admissible pair of irreducible reduced crystallographic root systems. By the duality symmetry, this gives rise to an…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
The Schur index in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with $U(N)$ gauge group has a natural two-parameter deformation. We find that a matrix integral in such a deformed Schur index can be exactly evaluated by using…
A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\leq N\leq 4$ supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to…
We extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle $FLM\to LM$ over the loop space of a Riemannian manifold $M$. Chern-Simons forms are…
Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points \cite{Giombi:2011kc}. These theories, particularly those based on bifundamental matter, are…
We show that every multilinear map between Euclidean spaces induces a unique, continuous, Minkowski multilinear map of the corresponding real cones of zonoids. Applied to the wedge product of the exterior algebra of a Euclidean space, this…
In this paper, we introduce a family of partially symmetric polynomials, which we call quantum corner polynomials, as a generalization of the Sergeev-Veselov super Macdonald polynomials. We show that these quantum corner polynomials are…
We describe an effective method for calculating certain infinite sums, generalizations of the classical Bernoulli polynomials. As shown by Edward Witten in his papers on two-dimensional gauge theories, the correlation functions of…
Using the theory of Macdonald, Gordon showed that the graded characters of the simple modules for the restricted rational Cherednik algebra by Etingof and Ginzburg associated to the symmetric group $\mathfrak{S}_n$ are given by…
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
We consider simple modules over the McConnell--Pettit algebras. We show that both induction and contraction yield simple modules for the extremes of the global dimension.
In this work, we present the three-dimensional Maxwell Carroll gravity by considering the ultra-relativistic limit of the Maxwell Chern-Simons gravity theory defined in three spacetime dimensions. We show that an extension of the Maxwellian…