Related papers: Unitary dual of quasi-split $PGSO_8^E$
In this paper, we introduce a notion of ladder representations for split odd special orthogonal groups and symplectic groups over a non-archimedean local field of characteristic zero. This is a natural class in the admissible dual which…
We study the local theta correspondence for dual pairs of the form $\mathrm{Aut}(C)\times F_{4}$ over a $p$-adic field, where $C$ is a composition algebra of dimension 2 or 4, by restricting the minimal representation of a group of type…
In this paper we consider a special class of arithmetic quotients of bounded symmetric domains which can roughly be described as higher- dimensional analogues of the Hilbert modular varities. The algebraic groups are defined as the unitary…
We develop an elementary divisor theory for the unimodular and the modular group over quadratic field extensions and quaternion algebras. In particular, we investigate which sets of elementary divisors can occur. Under an additional…
In \cite{JKS} we gave an (additive) categorification of Grassmannian cluster algebras, using the category $\CM(A)$ of Cohen-Macaulay modules for a certain Gorenstein order $A$. In this paper, using a cluster tilting object in the same…
In terms of highest weights, we establish branching rules for finite dimensional unitary simple modules of the general linear Lie superalgebra $\mathfrak{gl}_{m|n}$. Our proof uses the Howe duality for $\mathfrak{gl}_{m|n}$, as well as…
A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…
We construct the well-known decomposition of the Lie algebra $\mathfrak{e}_8$ into representations of $\mathfrak{e}_6\oplus\mathfrak{su}(3)$ using explicit matrix representations over pairs of division algebras. The minimal representation…
In this paper, we study the singularly perturbed Gaussian unitary ensembles defined by the measure \begin{equation*} \frac{1}{C_n} e^{- n\textrm{tr}\, V(M;\lambda,\vec{t}\;)}dM, \end{equation*} over the space of $n \times n$ Hermitian…
In this paper we prove the Aubert-Baum-Plymen-Solleveld conjecture for the split classical groups and establish the connection with the Langlands correspondence. To do this, we review the notion of cuspidality for enhanced Langlands…
By normalizing the space of commuting pairs of elements in a reductive Lie group G, and the corresponding space for the Langlands dual group, we construct pairs of hyperkahler orbifolds which satisfy the conditions to be mirror partners in…
We demonstrate that in N=8 supersymmetric mechanics with linear and nonlinear chiral supermultiplets one may dualize two auxiliary fields into physical ones in such a way that the bosonic manifold will be a hyper-Kaehler one. The key point…
We study the unitary supermultiplets of the N=4 d=7 anti-de Sitter (AdS_7) superalgebra OSp(8^*|4), with the even subalgebra SO(6,2) X USp(4), which is the symmetry superalgebra of M-theory on AdS_7 X S^4. We give a complete classification…
If for a vector space V of dimension g over a characteristic zero field we denote by $\wedge^iV$ its alternating powers, and by $V^\vee$ its linear dual, then there are natural Poincar\'e isomorphisms: $\wedge^i V^\vee \cong \wedge^{g-i}…
We show how, using different decompositions of E(11), one can calculate the representations under the duality group of the so--called "de-form" potentials. Evidence is presented that these potentials are in one-to-one correspondence to the…
We classify Jet modules for the Lie (super)algebras $\mathfrak{L}=W\ltimes(\mathfrak{g}\otimes\mathbb{C}[t,t^{-1}])$, where $W$ is the Witt algebra and $\mathfrak{g}$ is a Lie superalgebra with an even diagonlizable derivation. Then we give…
In this paper we use Weil conjectures (Deligne's theorem) to calculate the Betti numbers of the moduli spaces of semi-stable parabolic bundles on a curve. The quasi parabolic analogue of the Siegel formula, together with the method of…
By a local geometric Langlands correspondence for a complex reductive group G we understand a construction which assigns to a local system on the punctured disc for the Langlands dual group of G, a category equipped with an action of the…
We consider the octonionic self-duality equations on eight-dimensional manifolds of the form $M_8=M_4\times \R^4$, where $M_4$ is a hyper-K\"ahler four-manifold. We construct explicit solutions to these equations and their symmetry…
In this paper, we develop two new homological invariants called relative dominant dimension with respect to a module and relative codominant dimension with respect to a module. These are used to establish precise connections between Ringel…