Related papers: Symplectic determinant laws and invariant theory

We propose alternative determinant representations of certain form factors and scalar products of states in rational Gaudin models realized in terms of compact spins. We use alternative pseudo-vacuums to write overlaps in terms of partition…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

Infinite dimensional Hamiltonian systems appear naturally in the rich algebraic structure of Symplectic Field Theory. Carefully defining a generalization of gravitational descendants and adding them to the picture, one can produce an…

The goal of this paper is to extend the quiver Grassmannian description of certain degenerations of Grassmann varieties to the symplectic case. We introduce a symplectic version of quiver Grassmannians studied in our previous papers and…

Discovering symbolic differential equations from data uncovers fundamental dynamical laws underlying complex systems. However, existing methods often struggle with the vast search space of equations and may produce equations that violate…

The symplectic blob algebras are a family of finite dimensional noncommutative algebras over $\mathbb{Z}[X_1,X_2,X_3,X_4,X_5,X_6]$ that can be defined in terms of planar diagrams in a way that extends the Temperley-Lieb and (ordinary) blob…

In this paper, we consider the problem of representing a multivariate polynomial as the determinant of a definite (monic) symmetric/Hermitian linear matrix polynomial (LMP). Such a polynomial is known as determinantal polynomial.…

In this paper we study the determinant of irreducible representations of the generalized symmetric groups $\mathbb{Z}_r \wr S_n$. We give an explicit formula to compute the determinant of an irreducible representation of $\mathbb{Z}_r \wr…

Let G be a special orthogonal group or an inner form of a symplectic group over a number field F such that there exists a non-empty set S of real places of F at which G has discrete series and outside of which G is quasi-split. We prove…

In this paper, a description of the set-theoretical defining equations of symplectic (type C) Grassmannian/flag/Schubert varieties in corresponding (type A) algebraic varieties is given as linear polynomials in Pl$\ddot{u}$cker coordinates,…

This paper proves a version for stochastic differential equations of the Lie-Scheffers Theorem. This result characterizes the existence of nonlinear superposition rules for the general solution of those equations in terms of the involution…

This is a part of an ongoing project, the goal of which is to classify all semi-direct products $\mathfrak s=\mathfrak g{\ltimes} V$ such that $\mathfrak g$ is a simple Lie algebra, $V$ is a $\mathfrak g$-module, and $\mathfrak s$ has a…

In this paper, we define the concept of the Study-type determinant, and we present some properties of these determinants. These properties lead to some properties of the Study determinant. The properties of the Study-type determinants are…

A positive definite symmetric matrix {\sigma} qualifies as a quantum mechanical covariance matrix if and only if {\sigma}+(1/2)i\hbar{\Omega}\geq0 where {\Omega} is the standard symplectic matrix. This well-known condition is a strong…

Determinantal polynomials play a crucial role in semidefinite programming problems. Helton-Vinnikov proved that real zero (RZ) bivariate polynomials are determinantal. However, it leads to a challenging problem to compute such a…

We consider the restriction and induction of representations between a covering group and its derived subgroup, both on the representation-theoretic side and the L-parameter side. In particular, restriction of a genuine principal series is…

We give one more proof of the fact that symplectic matrices over real and complex fields have determinant one. While this has already been proved many times, there has been lasting interest in finding an elementary proof. Our result is…

The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this…

Symplectic vector spaces are the phase spaces of linear mechanical systems. The symplectic form describes, for example, the relation between position and momentum as well as current and voltage. The category of linear Lagrangian relations…

We study non-terminating graph rewriting models, whose local rules are applied non-deterministically -- and yet enjoy a strong form of determinism, namely space-time determinism. Of course in the case of terminating computation it is…