Related papers: Fermionic formulas for level-restricted generalize…
The recently modified Faddeev-Jackiw formalism for systems having one chain of four levels of only second-class constraints is applied to the non-trivial a=1 bosonized chiral Schwinger model in (1+1) dimensions as well as to one mechanical…
We use Kashiwara-Nakashima's combinatorics of crystal graphs associated to the roots sytems $B_{n}$ and $D_{n}$ to extend the results of \QCITE{cite}{}{lec3} and \QCITE{cite}{}{Mor} by showing that Morris type recurrence formulas also exist…
The level two string functions are calculated exactly for all simply laced Lie algebras, using a ladder coset construction. These are the characters of cosets of the type $G/U(1)^r$, where $G$ is the algebra at level two and $r$ is its…
We provide $\mathbb{N}$-filtrations on the negative part $U_q(\mathfrak{n}^-)$ of the quantum group associated to a finite-dimensional simple Lie algebra $\mathfrak{g}$, such that the associated graded algebra is a skew-polynomial algebra…
We study a class of representations called ``calibrated representations'' of the degenerate double affine Hecke algebra and those of the rational Cherednik algebra of type ${\mathrm{GL}}_n$. We give a realization of calibrated irreducible…
Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The…
We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a…
In this paper, we study two generalized constrained integrable hierarchies, which are called the $c$-$k$ constrained KP and BKP hierarchies. The Fermionic picture of the $c$-$k$ constrained KP hierarchy is given. We give some solutions for…
We consider a second degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting in its quantum…
In this paper we are concerned with the stabilization of MUSCL-type finite volume schemes in arbitrary space dimensions. We consider a number of limited reconstruction techniques which are defined in terms inequality-constrained linear or…
We give a purely combinatorial proof of the positivity of the stabilized forms of the generalized exponents associated to each classical root system. In finite type A_{n-1}, we rederive the description of the generalized exponents in terms…
In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new…
We present a fermionic description of non-equilibrium multi-level systems. Our approach uses the Keldysh path integral formalism and allows us to take into account periodic drives, as well as dissipative channels. The technique is based on…
We study gradient bounds and other functional inequalities for the diffusion semigroup generated by Kolmogorov type operators. The focus is on two different methods: coupling techniques and generalized $\Gamma$-calculus techniques. The…
We define and calculate versions of complexity for free fermionic quantum field theories in 1+1 and 3+1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits. We do this both by discretizing and identifying…
We study two different one-parameter generalizations of Littlewood--Richardson coefficients, namely Hall polynomials and generalized inverse Kostka polynomials, and derive new combinatorial formulae for them. Our combinatorial expressions…
Semiclassical limits of generic multiparameter quantized coordinate rings A = O_q(k^n) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric…
We study the restrictions of simple modules of Ariki-Koike algebras $\H_m(\v)$ with set of parameters $\v= (\zeta;\zeta^{v_0},... ,\zeta^{v_{l-1}})$, where $\zeta$ is an $n$th root of unity, to their subalgebras $\H_{m-j}(\v)$. Using a…
In the present work, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of new monogenic polynomials are provided based on 2-parameters weight functions. Such classes extend the well…
Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of $r$-spin intersection numbers. We represent this GKMM in terms of fermions and expand it in terms of the Schur polynomials by…