Related papers: Fermionic characters for graded parafermions

Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general…

Nonlinear fermions of degree $n$ ($n$-fermions) are introduced as particles with creation and annihilation operators obeying the simple nonlinear anticommutation relation $AA^\dagger + {A^\dagger}^n A^n = 1$. The ($n+1$)-order nilpotency of…

We present generalized Rogers-Ramanujan identities which relate the fermi and bose forms of all the characters of the superconformal model $SM(2,4\nu).$ In particular we show that to each bosonic form of the character there is an infinite…

We show that the characters of tilting modules can be used, in a concrete and explicit way, to obtain the simple characters of a connected reductive algebraic group $G$ over an algebraically closed field $\Bbbk$ of characteristic $p$, for…

We show that a simple change of the classical boson-fermion coupling constant, $2\alpha \to 2\alpha n $, $n\in \N$, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum…

We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation $\pi$ of a connected reductive $p$-adic group, subject to the assumption that $\pi$ is obtained via induction from a representation of…

In the quantum theory, using the notion of partial supersymmetry, in which some, but not all, operators have superpartners we derive the Euler theorem in partition theory. The paraferminic partition function gives another identity in…

We formulate a $\mathbb{Z}_k$-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising…

We derive new fermionic expressions for the characters of the Virasoro minimal models $M(k,2k\pm1)$ by analysing the recently introduced half-lattice paths. These fermionic expressions display a quasiparticle formulation characteristic of…

In this paper we give a new formula for characters of finite dimensional irreducible $\frak{gl}(m,n)$ modules. We use two main ingredients: Su-Zhang formula and Brion's theorem.

In an earlier paper [1] it was shown that the Frobenius compound characters for the symmetric groups are related to the irreducible characters by a linear relation that involves a unitriagular coupling matrix that gives the Frobenius…

This is the first of two articles devoted to the analysis of the path description of the states in su(2)_k WZW models, a representation well suited for constructive derivations of the fermionic characters. In this first article, the cases…

Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which…

We interpret aspects of the Schur indices, that were identified with characters of highest weight modules in Virasoro $(p,p')=(2,2k+3)$ minimal models for $k=1,2,\dots$, in terms of paths that first appeared in exact solutions in…

We study fermionic conformal field theories on surfaces with spin structure in the presence of boundaries, defects, and interfaces. We obtain the relevant crossing relations, taking particular care with parity signs and signs arising from…

In the first section we study a functor of Bezrukavnikov, Finkelberg and Ostrik defined on character sheaves; we compute it in a Grothendieck group taking weights into account. In the second section we enlarge the class of character sheaves…

Using the bases of principal subspaces for twisted affine Lie algebras except $A_{2l}^{(2)}$ by Butorac and Sadowski, we construct bases of the highest weight modules of highest weight $k\Lambda_0$ and parafermionic spases for the same…

We derive the fermionic polynomial generalizations of the characters of the integrable perturbations $\phi_{2,1}$ and $\phi_{1,5}$ of the general minimal $M(p,p')$ conformal field theory by use of the recently discovered trinomial analogue…

We enumerate generalizations of the superintegrability property $<character>\ \sim {\rm character}$ and illuminate possible general structures behind them. We collect variations of original formulas available up to date and emphasize the…

Superstrings have been postulated based on parafermionic partition functions which permit spacetime supersymmetry by generalized Jacobi identities. A comprehensive search finds new such identities. Quadrilateral anomaly cancellation gives…