Related papers: Binary Hermitian forms over a cyclotomic field

In this note, we compute Hirota bilinear forms arising from both homogeneous and principal realization of vertex representations of 2-toroidal Lie algebras of type $A_l, D_l, E_l$.

For each of the groups $G = O(2), SU(2), U(2)$, we compute the integral and $\mathbb{F}_2$-cohomology rings of $B_\text{com} G$ (the classifying space for commutativity of $G$), the action of the Steenrod algebra on the mod 2 cohomology,…

A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…

We derive explicit isomorphisms between certain congruence subgroups of the Siegel modular group, the Hermitian modular group over an arbitrary imaginary-quadratic number field and the modular group over the Hurwitz quaternions of degree 2…

We provide a diagrammatic computation for the bilinear form, which is defined as the pairing between the (relative) cup products with every local coefficients and every integral homology 2-class of every links in the 3-sphere. As a…

A general Vorono\"i summation formula for the (metaplectic) double cover of $\text{GL}_2$ is derived via the representation theoretic framework \`a la Ichino--Templier. The identity is also formulated classically and used to establish…

We define the category of $G_2$-structures over a Riemannian 7-manifold $M$ and present an isomorphism between this category and a full subcategory of the category of octonion algebras over the ring of smooth real-valued functions…

For a prime number $p$ and a free pro-$p$ group $G$ on a totally ordered basis $X$, we consider closed normal subgroups $G^\Phi$ of $G$ which are generated by $p$-powers of iterated commutators associated with Lyndon words in the alphabet…

A permutohedral variety is a remarkable object in various areas of mathematics, and its topological invariants are widely recognized. However, only little is known about a real permutohedral variety, that is, the real locus of a…

We classify quantum analogues of actions of finite subgroups G of SL_2(k) on commutative polynomial rings k[u,v]. More precisely, we produce a classification of pairs (H,R), where H is a finite dimensional Hopf algebra that acts inner…

We provide combinatorial rules to compute Kazhdan--Lusztig polynomials for the Hermitian symmetric pair $(B_N,A_{N-1})$ when the Hecke algebra has unequal parameters. They are obtained by filling regions delimited by paths with ballot…

We extend the result of Blumberg and Mandell on K-theoretic Tate-Poitou duality at odd primes which serves as a spectral refinement of the classical arithmetic Tate-Poitou duality. The duality is formulated for the $K(1)$-localized…

We construct the quantum double ramification hierarchy associated with the Gromov-Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the double ramification cycle, the Gromov-Witten…

Let $\phi:\Z/p\to GL_{n}(\Z)$ denote an integral representation of the cyclic group of prime order $p$. This induces a $\Z/p$-action on the torus $X=\R^{n}/\Z^{n}$. The goal of this paper is to explicitly compute the cohomology groups…

In this article, the matrix elements of a representation of the 5-dimensional Lie algebra K5 are obtained for the first time. The bivariate degenerate Hermite polynomials Hm(z1, z2|{\tau} ) are considered within the context of this…

We show that the de Rham complex of any almost Hermitian manifold carries a natural commutative $BV_\infty$-algebra structure satisfying the degeneration property. In the almost K\"ahler case, this recovers Koszul's BV-algebra, defined for…

Let $G$ be a finite group and let $k$ be a sufficiently large finite field. Let $R(G)$ denote the character ring of $G$ (i.e. the Grothendieck ring of the category of ${\mathbb{C}}G$-modules). We study the structure and the representations…

We construct a Hopf algebra on integer binary relations that contains under the same roof several well-known Hopf algebras related to the permutahedra and the associahedra: the Malvenuto-Reutenauer algebra on permutations, the Loday-Ronco…

Using the orbifold KZ connection we construct a functor from an affine parabolic category O of type A to the category O of a cyclotomic rational double affine Hecke algebra. We give several results concerning this functor.

We discuss the only two viable realizations of fermion compositeness described by a calculable relativistic effective field theory consistent with unitarity, crossing symmetry and analyticity: chiral-compositeness vs…