相关论文: From Cauchy's determinant formula to bosonic and f…
We study a matrix that arises from a singular form of the Woodbury matrix identity. We present generalized inverse and pseudo-determinant identities for this matrix, which have direct applications for Gaussian process regression,…
The three dimensional abelian fermionic determinant of a two component massive spinor in flat euclidean space-time is resetted to a pure Chern-Simons action through a nonlinear redefinition of the gauge field.
In this work, the determinants of matrices constructed by evaluating homogeneous bivariate polynomials at pairs of vectors are investigated. For a polynomial $p(x,y)=\sum\limits_{i=0}^k \alpha_i x^{k-i}y^i$, an explicit factorization of the…
The Hilbert space of an RSOS-model, introduced by Andrews, Baxter, and Forrester, can be viewed as a space of sequences (paths) {a_0,a_1,...,a_L}, with a_j-integers restricted by 1<=a_j<=\nu, |a_j-a_{j+1}|=1, a_0=s, a_L=r. In this paper we…
The main result of this paper is two infinity classes of series-product identities which is based on classical Gauss identity and two different interpretations of character formula for irreducible highest weight modules of affine Lie…
We introduce Fermi Sets, a universal and physically interpretable neural architecture for fermionic many-body wavefunctions. Building on a ``parity-graded'' representation [1], we prove that any continuous fermionic wavefunction on a…
We consider the linearization of $N = 1$ nonlinear supersymmetry (NLSUSY) based on a commutator algebra in Volkov-Akulov NLSUSY theory. We show explicitly that $U(1)$ gauge and scalar supermultiplets in addition to a vector supermultiplet…
The identification mentioned in the title allows a formulation of the multidi mensional Favard Lemma different from the ones currently used in the literature and which exactly parallels the original one dimensional formulation in the sense…
We introduce an algebraic model, based on the determinantal expansion of the product of two matrices, to test combinatorial reductions of set functions. Each term of the determinantal expansion is deformed through a monomial factor in d…
A formula expressing the fermionic determinant as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and are indexed by loops of…
We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.
Results providing conditions on a family of integro-differential operators to determine a formal automorphism are established. Equivalently, the problem can be read in terms of existence and uniqueness of formal solutions of Cauchy problems…
We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosonic and fermionic partner Hamiltonians. Due to the…
The structure function of a random matrix ensemble can be specified as the covariance of the linear statistics $\sum_{j=1}^N e^{i k_1 \lambda_j}$, $\sum_{j=1}^N e^{-i k_2 \lambda_j}$ for Hermitian matrices, and the same with the eigenvalues…
Differential operators commuting with integral operators were discovered in the work of C. Tracy and H. Widom [37, 38] and used to derive asymptotic expansions of the Fredholm determinants of integral operators arising in random matrix…
We consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the…
The present paper is a detailed version of math/0003031. We introduce and study a new basis in the algebra of symmetric functions. The elements of this basis are called the Frobenius-Schur functions (FS-functions, for short). Our main…
In our previous works, a relationship between Hermite's two approximation problems and Schlesinger transformations of linear differential equations has been clarified. In this paper, we study tau-functions associated with holonomic…
We apply the Desnanot-Jacobi identity to give an alternative proof of the determinants whose entries are rising powers of the Fibonacci numbers given by Prodinger. We then generalize the determinants to include entries that are rising…
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…