Related papers: Mock plectic points
In this paper we use the technique of Hopf algebras and quasi-symmetric functions to study the combinatorial polytopes. Consider the free abelian group $\mathcal{P}$ generated by all combinatorial polytopes. There are two natural bilinear…
In this paper we consider the integral orthogonal group with respect to the quadratic form of signature $(2,3)$ given by $\left(\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix}\right) \perp \left(\begin{smallmatrix} 0 & 1 \\ 1 & 0…
We introduce the symplectic group $\mathrm{Sp}_2(A,\sigma)$ over a noncommutative algebra $A$ with an anti-involution $\sigma$. We realize several classical Lie groups as $\mathrm{Sp}_2$ over various noncommutative algebras, which provides…
This article presents a comprehensive study of \textit{Kirchhoff-type Critical Elliptic Equations} involving $p$-sub-Laplacian Operators on the \textit{Heisenberg Group} $\mathcal{H}_{n}$. It delves into the mathematical framework of…
In this paper, we study the parallel cases of Zagier's and Folsom-Ono's grids of weakly holomorphic (resp. weakly holomorphic and mock modular) forms of weights 3/2 and 1/2, investigating their $p$-adic properties under the action of Hecke…
The endomorphism algebras of the permutation modules for transitive permutation groups, known as Hecke algebras, are fundamental objects in representation theory. While group algebras are known to be symmetric over any field, it is natural…
We undertake a study of topological properties of the real Mordell-Weil group $\operatorname{MW}_{\mathbb R}$ of real rational elliptic surfaces $X$ which we accompany by a related study of real lines on $X$ and on the "subordinate" del…
We study moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras. The resulting symplectic manifolds are closely related with Poisson-Lie groups and their algebraic structure…
We consider the groups G which arise from real semisimple Jordan algebras via the Tits-Koecher-Kantor construction. Such a G is characterized by the fact that it admits a parabolic subgroup P=LN which is conjugate to its opposite, and for…
We define the notion of a $G$-structure for elliptic curves, where $G$ is a finite 2-generated group. When $G$ is abelian, a $G$-structure is the same as a classical congruence level structure. There is a natural action of…
The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is…
We give the values of the Siegel-Veech constants associated with saddle connections having distinct endpoints on translation surfaces in Prym eigenform loci in $\Omega \mathcal{M}_3(2,2)^{\rm odd}$. In particular, we show that these…
The aim of the paper is to prove the following result concerning moduli of curve families in the Heisenberg group. Let $\Omega$ be a domain in the Heisenberg group foliated by a family $\Gamma$ of legendrian curves. Assume that there is a…
Let $\M_g$ be the course moduli space of complex projective nonsingular curves of genus $g$. We prove that when the Brill-Noether number $\rho(g,1,n)$ is non-negative the Petri locus $P^1_{g,n}\subset \M_g$ has a divisorial component whose…
We study the Selmer group associated to a $p$-ordinary newform $f \in S_{2r}(\Gamma_0(N))$ over the anticyclotomic $\mathbb{Z}_p$-extension of an imaginary quadratic field $K/\mathbb{Q}$. Under certain assumptions, we prove that this Selmer…
The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\Z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…
In the study of the arithmetic structure of elliptic modular groups which are the fundamental groups of compactified modular curves, these truncated group algebras and their direct sums are considered to construct elliptic modular motives.…
Let H_q(S_n) be the Iwahori-Hecke algebra of the symmetric group. This algebra is semisimple over the rational function field Q(q), where q is an indeterminate, and its irreducible representations over this field are q-analogues S_q(lambda)…
We study a factor Hopf algebra $\mathfrak{PP}$ of the Malvenuto-Reutenauer convolution algebra of functions on symmetric groups ${\mathfrak{S}}=\oplus_{n\geq 0} \mathbb C[{\mathfrak{S}}_n] $ that we coined pre-plactic algebra. The…
We compute the Picard group $ Pic(A_q) $ of the noncommutative algebraic 2-torus $A_q$, describe its action on the space $ R(A_q) $ of isomorphism classes of rk 1 projective modules and classify the algebras Morita equivalent to $ A_q $.…