Related papers: Sub-Shimura Varieties for type O(2,n)
This is the fourth one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups of minus type.
The aim of the present short note is to answer the open questions posted by Hern\'andez, Martin, and Rodrigues in {\rm \cite{p1,p2}}. The obtained results give the complete classification of irreducible components in the varieties of Jordan…
We describe the quantum cohomology rings of a class of toric varieties. The description includes, in addition to the (already known) ring presentations, the (new) analogues for toric varieties of the sorts of quantum Giambelli formulas…
In this paper, we investigate a general method to establish tame and norm relations for special cycles in Shimura varieties, using unitary cycles in odd orthogonal Shimura varieties as a guiding example.
We describe work of Faltings on the construction of \'etale cohomology classes associated to symplectic Shimura varieties and show that they satisfy certain trace compatibilities similar to the ones of Siegel units in the modular curve…
We compute the level groups associated with mixed Shimura varieties that appear at the boundaries of compactifications of Shimura varieties and show that the boundaries of minimal compactifications of Pappas-Rapoport integral models are…
The automorphic cohomology of a connected reductive algebraic group defined over Q decomposes as a direct algebraic sum of cuspidal and Eisenstein cohomology. In the present paper we construct regular Eisenstein cohomology classes for…
We study commutative Schur rings over the symplectic groups Sp$(n,2)$ containing the class $\mathcal C$ of symplectic transvections. We find the possible partitions of $\mathcal C$ determined by the Schur ring. We show how this restricts…
We complete the classification of quantum subgroups of $SL_q(2)$ with $q$ a root of unity of arbitrary order, that is, Hopf algebra quotients of the quantum function algebras $\mathcal{O}_{q} (SL_2(\mathbb{C}))$.
We give a computationally effective criterion for determining whether a finite-index subgroup of SL(2, Z) is a congruence subgroup, extending earlier work of Hsu for subgroups of PSL(2, Z).
We investigate several classes of submanifolds of almost quaternionic skew-Hermitian manifolds $(M^{4n}, Q, \omega)$, including almost symplectic, almost complex, almost pseudo-Hermitian and almost quaternionic submanifolds. In the…
In this paper we study representations of the indefinite orthogonal group O(n,m) which are local theta lifts of one dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. We apply the transfer…
We study a family of subrings, indexed by the natural numbers, of the mod-p cohomology of a finite group G. These subrings are based on a family of v_n-periodic complex oriented cohomology theories and are constructed as rings of…
In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class.
Some years ago, Borcherds described in [Bo1] two methods for constructing modular forms on modular varieties related to the orthogonal group ${\O}(2,n)$. They are the so called Borcherds' additive and multiplicative lifting. The…
In this paper, we present a simple proof of the fact that any compact subgroup of homeomorphisms of the 2-sphere is topologically conjugate to a closed subgroup of the orthogonal group O(3).
We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature $(n+1,1)$ and prove that they are holomorphic Hermitian modular forms.…
This is a follow-up to the paper in which we categorified the affine quantum Schur algebra S(n,r) for 2 < r < n, using a quotient of Khovanov and Lauda's categorification of the affine quantum sl_n. In this paper we categorify S(n,n) for n…
We study vector-valued Siegel modular forms of genus 2 and level 2. We describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued modular forms.
We show the existence of two new Shimura subvarieties of $\mathcal{A}_2, \mathcal{A}_3$ generically contained in the Torelli locus. They provide the first examples of Shimura subvarieties obtained by means of Jacobians carrying non-trivial…