Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

We investigate the curvature operator of second kind on Riemannian manifolds and prove several classification results. The first one asserts that a closed manifold with three-positive is diffeomorphic to spherical space form, improving recent result Cao-Gursky-Tran assuming two-positivity. states three-nonnegative either or flat, isometric quotient compact irreducible symmetric space. This sett...

Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider an ordered pair of linear transformations A : V → V and A : V → V which satisfy the following two properties: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V wi...

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...

Let C be a smooth projective irreducible curve defined over a finite field k. Let G be a finite subgroup of Aut(C) of order prime to char(k) and M the |G|-th cyclotomic field. We show that certain idempotent relations in M [G] imply relations among arithmetic invariants of the fundamental groups of the quotient curves (C/H)×k k, where H is a subgroup of G.

The number A(q) shows the asymptotic behaviour of the quotient of the number of rational points over the genus of non-singular absolutely irreducible curves over IFq . Research on bounds for A(q) is closely connected with the so-called asymptotic main problem in Coding Theory. In this paper, we study some generalizations of this number for nonirreducible curves, their connection with A(q) and i...

Let Y be an Enriques variety of complex dimension 2n − 2 with n ≥ 2. Assume that n = 2m for odd prime m. In this paper we show that Y is the quotient of a product of a Calabi-Yau manifold of dimension 2m and an irreducible holomorphic symplectic manifold of dimension 2m − 2 by an automorphism of order n acting freely. We also show that both Y and its universal cover are always projective.

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...

In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applications of our result including the construction of a sort of Gelfand–Zeitlin basis for a generic irreducible representation of Uq(GL(n)) when q is a primitive odd root of unity. 2010 Math. Subj. Class. 20G07,...

We show that in ADE type the trace of Webster's categorification a tensor product irreducibles for quantum group is isomorphic to Weyl modules current algebra U˙(g[t]). This extends result Beliakova, Habiro, Lauda, and Webster who showed categorified U˙⁎(g) U˙(g[t]), cyclotomic quotient U˙⁎(g), which categorifies single irreducible group, module use deformation argument based on technique unfur...