Related papers: A remark on two duality relations
We prove the little Grothendieck theorem for any 2-convex noncommutative symmetric space. Let $\M$ be a von Neumann algebra equipped with a normal faithful semifinite trace $\t$, and let $E$ be an r.i. space on $(0, \8)$. Let $E(\M)$ be the…
We prove the Volume Conjecture for the relative Reshetikhin-Turaev invariants proposed in [29] for all pairs (M,K) such that M\K is homeomorphic to the complement of the figure-8 knot in S^3 with almost all possible cone angles.
A field $K$ is $d$-local if there exist fields $K=k_d,...,k_0$ with $k_{i+1}$ complete discrete valuation with residue field $k_i$, and $k_0$ finite of characteristic $p$. By work of Deninger and Wingberg, the Galois cohomology of such…
Xu, Yan and Zhao showed that in even weight, the multiple $T$ value $T(2, 1, \ldots, 1, \overline{1})$ is a polynomial in $\log(2)$, $\pi$, Riemann zeta values, and Dirichlet beta values. Based on low-weight examples, they conjectured that…
We prove a criterion for continuity of bilinear maps on countable direct sums of topological vector spaces. As a first application, we get a new proof for the fact (due to Hirai et al. 2001) that the map taking a pair of test functions on…
In "All p-adic reductive groups are tame" Bernstein proved that for a reductive group G over a local non-archimedean field F and a compact open subgroup K of G there exists a uniform bound N(G,K) such that for every irreducible, smooth, and…
The present paper investigates a natural generalization of the duality between Riemannian symmetric pairs of compact type and those of non-compact type \`a la \'E. Cartan. The main result of this paper is to construct an explicit…
Let $i(n,k)$ be the proportion of permutations $\pi\in\mathcal{S}_n$ having an invariant set of size $k$. In this note we adapt arguments of the second author to prove that $i(n,k) \asymp k^{-\delta} (1+\log k)^{-3/2}$ uniformly for $1\leq…
Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = \sum_{n=0}^{\infty}T_u(n) in which D(u) denotes the defect of u and T_u(n) denotes C_u(n+1)-C_u(n) +2 - P_U(n+1) -…
Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular, simple self-contained proofs of their two key statements.…
We strongly believe that in order to prove two important geometrical pro\-blems in convexity, namely, the G. Bianchi and P. Gruber's Conjecture \cite{bigru} and the J. A. Barker and D. G. Larman's Conjecture \cite{Barker}, it is necessary…
We develop an algebraic formalism for topological $\mathbb{T}$-duality. More precisely, we show that topological $\mathbb{T}$-duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known…
We find the general form of supersymmetric invariant two point functions. By imposing supersymmetric positivity we obtain the general supersymmetric K\"allen-Lehmann representation.
In this paper we give a study of the symmetrized divergences $U_s(p,q)=K_s(p||q)+K_s(q||p)$ and $V_s(p,q)=K_s(p||q)K_s(q||p)$, where $K_s$ is the relative divergence of type $s, s\in\mathbb R$. Some basic properties as symmetry,…
For any given set $A$ of nonnegative integers and for any given two positive integers $k_1,k_2$, $R_{k_1,k_2}(A,n)$ is defined as the number of solutions of the equation $n=k_1a_1+k_2a_2$ with $a_1,a_2\in A$. In this paper, we prove that if…
In this paper, we introduce the generalized Cauchy dual $w(T) = T(T^{*}T)^{\dagger}$ of a closed operator $T$ with the closed range between Hilbert spaces and present intriguing findings that characterize the Cauchy dual of $T$.…
We establish an $S$-duality converse to the one studied by the 1st, 2nd and 4th authors; this is also a case of a twisted version of the relative Langlands duality of Ben Zvi, Sakellaridis and Venkatesh.. Namely, we prove that the $S$-dual…
Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u)=\sum_{n=0}^{\infty} T(n) in which D(u) denotes the defect of u and T(n) denotes C(n+1)-C(n)+2-P(n+1)-P(n), where C…
By using various expansions of the parametric digamma function and the method of residue computations, we study three variants of the linear Euler sums, related Hoffman's double $t$-values and Kaneko-Tsumura's double $T$-values, and…
This paper is a continuation of [8], in the direction of proving the conjecture that the spherical transform on a nilpotent Gelfand pair (N,K) establishes an isomorphism between the space of K-invariant Schwartz functions on N and the space…