The set of n by n upper-triangular nilpotent matrices with entries in a finite field Fq has Jordan canonical forms indexed by partitions λ ` n. We study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number Fλ(q) of matrices of fixed Jordan type as a weighted sum over rook placements. Résumé. L’ensemble des matrices triang...

We show that the algebra homomorphism Uq(ĝln) ։ K GLd×C ∗ (Z)⊗C(q) constructed by Ginzburg and Vasserot between the quantum affine algebra of type gln and the equivariant K-theory group of the Steinberg variety (of incomplete flags), specializes to a surjective homomorphism U res ǫ (ĝln) ։ K GLd×C ∗ ǫ (Z). In particular, this shows that the parametrization of irreducible U res ǫ (ŝln)-modules a...

Let G and G be simple Lie groups of equal real rank and real rank at least 2. Let Γ < G and Λ < G be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of Γ into Λ is at bounded distance from a homomorphism. For example, any quasiisometric embedding of SL(n,Z) into SL(n,Z[i]) is at bounded distance from a homomorphism. We also include a discussion of ...

Participants pressed computer keys to keep a moving dot stimulus within a rectangle, either alone or with a partner they could neither see nor hear. Pressing the A-key or L-key caused the dot to move right or left, respectively, for as long as the key was pressed. Switching between the A and L keys (i.e., turning) proved challenging: concurrently pressing both keys made the stimulus move upward...

The paper attempts a systematic study of homomorphisms of relational structures. Such structures are modeled as multialgebras (i.e., relation is represented as a set-valued function). The rst, main, result is that, under reasonable restrictions on the form of the deenition of homomorphism, there are exactly nine compositional homomorphisms of multialgebras. Then the comparison of the obtained c...

Cloud computing is one of the widest phenomena embraced in information technology. This result from numerous advantages associated with it making many organizations and individuals offload their data to cloud. Encryption schemes restrict access unauthorized clients, helping attain confidentiality privacy. The modification ciphertext clients’ on cloud demand downloading, deciphering, editing, fi...

We present an efficient algorithm for obtaining a canonical system of Jordan chains for an n×n regular analytic matrix function A(λ) that is singular at the origin. For any analytic vector function b(λ), we show that each term in the Laurent expansion of A(λ)−1b(λ) may be obtained from the previous terms by solving an (n+d)× (n+d) linear system, where d is the order of the zero of detA(λ) at λ ...

in symplectic Floer homology. Both were discovered by Donaldson. They are well defined up to an overall sign. The homomorphism (1) can be interpreted as a relative Donaldson invariant on a 4-manifold with boundary. In other words, this product is obtained by counting anti-self-dual connections over a 4-dimensional cobordism with n+ 1 cylindrical ends corresponding to Yfj . The second homomorphi...