Related papers: Explicit Formulas for 2-Characters
We briefly discuss linear algebraic, combinatorial, and applied aspects of an exact model representation of binary arrays. As an illustration, we present two linear algebraic portraits of a string of characters.
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
We explore some interesting features of the characteristic polynomial of the Cartan matrix of a simple Lie algebra. The characteristic polynomial is closely related with the Chebyshev polynomials of first and second kind. In addition, we…
Let GO(2n) be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic not equal to 2. We determine the etale cohomology ring with mod 2 coefficients of the algebraic stack BGO(2n). In…
A general notion of detection is introduced and used in the study of the cohomology of elementary abelian 2-groups with respect to the spectra in the Postnikov tower of orthogonal K-theory. This recovers and extends results of Bruner and…
For $G$ a finite group, we show that functions on fields for the 2-dimensional supersymmetric sigma model with background $G$-symmetry determine cocycles for complex analytic $G$-equivariant elliptic cohomology. Similar structures in…
We obtain explicit formulas for the product of a deformed Weyl denominator with the character of an irreducible representation of the spin group $\rm{Spin}_{2r+1}({\mathbb C})$, which is an analogue of the formulas of Tokuyama for Schur…
In this paper, we obtain remainder term representation formulae for the higher-order Steklov inequality for vector fields which imply short and direct proofs of the sharp (classical) Steklov inequalities. The obtained results directly imply…
In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of…
Coorbit spaces provide a rigorous framework for the assessment of the approximation theoretic properties of generalized wavelet systems. It is therefore useful to understand when two different wavelet systems give rise to the same scales of…
We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite dimensional algebras. In particular, we define, construct and describe in detail (right) cell 2-representations…
Given any diagram of a link, we define on the cube of Kauffman's states a "2-complex" whose homology is an invariant of the associated framed links, and such that the graded Euler characteristic reproduces the unnormalized Kauffman bracket.…
Let $F$ be a field of characteristic $0$ and let $E$ be the infinite dimensional Grassmann algebra over $F$. In the first part of this paper we give an algorithm calculating the generating function of the cocharacter sequence of the…
We compute exact solutions of two--matrix models, i.e. detailed genus by genus expressions for the correlation functions of these theories, calculated without any approximation. We distinguish between two types of models, the unconstrained…
In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this…
Several characterizations of weak cotype 2 and weak Hilbert spaces are given in terms of basis constants and other structural invariants of Banach spaces. For finite-dimensional spaces, characterizations depending on subspaces of fixed…
In this paper we consider the character of a finite dimensional algebraic representation of $GL_{mn}({\mathbb C})$ restricted to a particular disconnected component of the normalizer of the Levi subgroup $GL_m({\mathbb C})^n$ of…
We characterize finite groups G generated by orthogonal transformations in a finite-dimensional Euclidean space V whose fixed point subspace has codimension one or two in terms of the corresponding quotient space V/G with its quotient…
Exactly integrable systems connected to semisimple algebras of second rank with an arbitrary choice of grading are presented in explicit form. General solutions of these systems are expressed in terms of matrix elements of two fundamental…
This paper introduces a notion of 2-orthogonality for a sequence of polynomials to give extended versions of the Meixner and Feinsilver characterization results based on orthogonal polynomials. These new versions subsume the Letac-Mora…