Related papers: A note on Samelson product in $Sp(n)$

For $(\mathbb{C} P^2 \# 5{\overline {\mathbb{C} P^2}},\omega)$, let $N_{\omega}$ be the number of $(-2)$-symplectic spherical homology classes.We completely determine the Torelli symplectic mapping class group (Torelli SMCG): the Torelli…

We consider the zero sets $Z_N$ of systems of $m$ random polynomials of degree $N$ in $m$ complex variables, and we give asymptotic formulas for the random variables given by summing a smooth test function over $Z_N$. Our asymptotic…

Let $m \in \mathbb{N}$ be large. We show that there exist infinitely many primes $q_{1}< \cdot\cdot\cdot < q_{m+1}$ such that \[ q_{m+1}-q_{1}=O(e^{7.63m}) \] and $q_{j}+2$ has at most \[ \frac{7.36m}{\log 2} + \frac{4\log m}{\log 2} + 21…

The n-dimensional projective group gives rise to a one-parameter family of inhomogeneous first-order differential operator representations of sl(n+1). By partially swapping differential operators and multiplication operators, we obtain more…

Fock space representations of the Lie superalgebra $sl(n+1|m)$ and of its quantum analogue $U_q[sl(n+1|m)]$ are written down. The results are based on a description of these superalgebras via creation and annihilation operators. The…

This paper contains some results about the topology of $\M_{0,n+1}/\Sigma_n$, where $\M_{0,n+1}$ is the moduli space of genus zero Riemann surfaces with marked points. We show that $\M_{0,n+1}/\Sigma_n$ is not a topological manifold for…

We study several properties of the symmetric power $S^mX$ of a smooth variety $X$. We describe the Picard and divisor class groups of $S^mX$ when $X$ is projective. We give a complete description of the stratification of $S^mX$ by iterated…

Let $0<m<n$ be integers, and let $K_w$ denote the completion of a number field $K$ at a non-trivial place $w$. For each non-zero $\textbf{u}\in K_w^n$, let $\omega_{m-1}(\textbf{u})$ denote the exponent of best approximation to $\textbf{u}$…

Let R: V x V -> V x V be a Hecke type solution of the quantum Yang-Baxter equation (a Hecke symmetry). Then, the Hilbert-Poincre' series of the associated R-exterior algebra of the space V is a ratio of two polynomials of degree m…

A Skolem sequence of order n is a sequence S_n=(s_{1},s_{2},...,s_{2n}) of 2n integers containing each of the integers 1,2,...,n exactly twice, such that two occurrences of the integer j in {1,2,...,n} are separated by exactly j-1 integers.…

Let $M_0(n)$ (resp. $M_1(n)$) denote the number of partitions of $n$ with even (reps. odd) crank. Choi, Kang and Lovejoy established an asymptotic formula for $M_0(n)-M_1(n)$. By utilizing this formula with the explicit bound, we show that…

The asymptotic form of the number of n-quasigroups of order 4 is $3^{n+1} 2^{2^n +1} (1+o(1))$. Keywords: n-quasigroups, MDS codes, decomposability, reducibility.

For every integer $k\geq 2$ let $[k]^{<\mathbb{N}}$ be the set of all words over $k$, that is, all finite sequences having values in $[k]:=\{1,...,k\}$. A Carlson-Simpson tree of $[k]^{<\mathbb{N}}$ of dimension $m\geq 1$ is a subset of…

Let s,t,m,n be positive integers such that sm=tn. Let M(m,s;n,t) be the number of m x n matrices over {0,1,2,...} with each row summing to s and each column summing to t. Equivalently, M(m,s;n,t) counts 2-way contingency tables of order m x…

Let $K/\mathbb{Q}$ be a quadratic extension. In this paper we study the $4$-rank of the class group $\text{Cl}(K(\sqrt{n}))$, where $n$ varies over squarefree rational integers. We show that for $100\%$ of squarefree $n$, the $4$-rank is…

Let $S_n$ and $S_{n,k}$ be, respectively, the number of subsets and $k$-subsets of $\mathbb{N}_n=\{1,\ldots,n\}$ such that no two subset elements differ by an element of the set $\mathcal{Q}$, the largest element of which is $q$. We prove a…

We study W-algebras obtained by quantum Hamiltonian reduction of $sl(Mn)$ associated to the $sl(2)$ embedding of rectangular type. The algebra can be realized as the asymptotic symmetry of higher spin gravity with $M \times M$ matrix valued…

We confirm a conjecture of Quillen in the case of the mod $2$ cohomology of arithmetic groups ${\rm SL}_2({\mathcal{O}}_{\mathbb{Q}(\sqrt{-m})}[\frac{1}{2}]\thinspace)$, where ${\mathcal{O}}_{\mathbb{Q}(\sqrt{-m}\thinspace)}$ is an…

We present an approach to solvable pseudo-Riemannian symmetric spaces based on papers of M.Cahen, M.Parker and N.Wallach. Thereby we reproduce the classification of solvable symmetric triples of Lorentzian signature $(1,n-1)$ and complete…

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an $n$-sample in a space $M$ can be…