Related papers: Another presentation for symplectic Steinberg grou…

We investigate the group structure of center-preserving automorphisms of the finite Heisenberg group over $\mathbb Z_N$ with $U(1)$ extension, which arises in finite-dimensional quantum mechanics on a discrete phase space. Constructing an…

The symmetries provided by representations of the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$ are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory…

We prove that linear groups over rings of non-commutative Laurent polynomials $D_{\tau}$ have Tits systems with the corresponding affine Weyl groups and have universal central extensions if $|Z(D)|\geq 5$ and $|Z(D)|\neq 9$. We also…

The purpose of the paper is to derive linkage principle for modular representations of ortho-symplectic supergroups. We follow the approach of Doty and investigate in detail the representation theory of the orthosymplectic group $OSP(2|1)$…

We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$, the derived and the stable categories…

We lay the foundations for a broad algebraic theory encompassing SICs in the hope of elucidating their heuristic connections with Stark units. What emerges is a greatly generalised set-up with added structure and potential for applications…

We give a definition of symplectic homology for pairs of filled Liouville cobordisms, and show that it satisfies analogues of the Eilenberg-Steenrod axioms except for the dimension axiom. The resulting long exact sequence of a pair…

We call a conjugacy class of the symplectic group Sp$(2n, K)$ over a field $K$ strictly hyperbolic if its minimal polynomial is of the form $q(x) q^*(x)$, where the polynomial $q(x)$ is prime to its reciprocal $q^*(x) := x^n q(x^{-1})$. It…

The symplectic group Sp(2g,Z) is a subgroup of the linear group SL(2g,Z) and admits a faithful action on the sphere S^(2g-1), induced from its linear action on Euclidean space R^(2g). Generalizing corresponding results for linear groups, we…

We explicitly realize an internal action of the symplectic cactus group, recently defined by Halacheva for any complex, reductive, finite-dimensional Lie algebra, on crystals of Kashiwara-Nakashima tableaux. Our methods include a symplectic…

We construct left invariant special K\"ahler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special K\"ahler Lie algebras according to two linear representations…

Let p be an odd prime number, E an elliptic curve over a number field k, and F/k a Galois extension of degree twice a power of p. We study the Z_p-corank rk_p(E/F) of the p-power Selmer group of E over F. We obtain lower bounds for…

In this paper we study a restricted family of holomorphic symplectic leaves in the Poisson-Lie group ${\rm GL}_r(\mathcal{K}_{\mathbb{P}^1_x})$ with rational quadratic Sklyanin brackets induced by a one-form with a single quadratic pole at…

In this paper, we introduce a new kind of Siegel upper half space and consider the symplectic geometry on it explicitly under the action of the group of all holomorphic transformations of it. The results and methods will form a basis for…

Let $K/k$ be a finite Galois CM-extension of number fields whose Galois group $G$ is monomial and $S$ a finite set of places of $k$.\ Then the "Stickelberger element" $\theta_{K/k,S}$ is defined.\ Concerning this element,\ Andreas Nickel…

Let $G$ be a simply connected simple algebraic group. The classical multiplicative and additive Grothendieck-Springer resolutions are simultaneous resolutions of singularities for the maps from $G$ and its Lie algebra to their invariant…

In this paper we prove Schur-Weyl duality between the symplectic group and Brauer algebra over an arbitrary infinite field $K$. We show that the natural homomorphism from the Brauer algebra $B_n(-2m)$ to the endomorphism algebra of tensor…

We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a quantization of a conical symplectic…

We consider a finite abelian group $M$ of odd exponent $n$ with a symplectic form $\omega: M\times M\to \mu_n$ and the Heisenberg extension $1\to \mu_n\to H\to M\to 1$ with the commutator $\omega$. According to the Stone - von Neumann…

The algebra of holomorphic polynomial Sp_{2n}-invariants of k complex 2n by 2n matrices (under diagonal conjugation action) is generated by the traces of words in these matrices and their symplectic adjoints. No concrete minimal generating…