Related papers: The Gamma filtrations for the Spin groups

Given a spin rational homology sphere $Y$ equipped with a $\mathbb{Z}/m$-action preserving the spin structure, we use the Seiberg--Witten equations to define equivariant refinements of the invariant $\kappa(Y)$ from \cite{Man14}, which take…

For generic time-reversal invariant systems with spin-orbit couplings, we clarify a close relationship between the Z$_2$ topological order and the spin Chern number proposed by Kane and Mele and by Sheng {\it et al.}, respectively, in the…

Let $G$ be the alternating group of degree $n$. Let $\omega(G)$ be the maximal size of a subset $S$ of $G$ such that $\langle x,y \rangle = G$ whenever $x,y \in S$ and $x \neq y$ and let $\sigma(G)$ be the minimal size of a family of proper…

We give a generalization to higher genera of the famous formula $12 \lambda=\delta$ for genus 1. We also compute the classes of certain strata in the Satake compactification as elements of the push down of the tautological ring.

For several natural filtrations of a free group S we express the n-th term of the filtration as the intersection of all kernels of homomorphisms from S to certain groups of upper-triangular unipotent matrices. This generalizes a classical…

Recent discoveries make it possible to compute the K-theory of certain rings from their cyclic homology and certain versions of their cdh-cohomology. We extend the work of G. Corti\~nas et al. who calculated the K-theory of, in addition to…

A classification is given of the exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptional compact Lie group or $S\!pin(8)$, and moreover the structure of $K$ is determined as Lie…

In this article we describe the $\tG\times \tG$-equivariant $K$-ring of $X$, where $\tG$ is a {\it factorial} cover of a connected complex reductive algebraic group $G$, and $X$ is a regular compactification of $G$. Furthermore, using the…

Following the quantisation of a graph with the Dirac operator (spin-1/2) we explain how additional weights in the spectral form factor K(\tau) due to spin propagation around orbits produce higher order terms in the small-\tau asymptotics in…

Let $G/H$ be a reductive symmetric space of split rank $1$ and let $K$ be a maximal compact subgroup of $G$. In a previous article the first two authors introduced a notion of cusp forms for $G/H$. We show that the space of cusp forms…

Let G be a connected real reductive group. Orbit integrals define traces on the group algebra of G. We introduce a construction of higher orbit integrals in the direction of higher cyclic cocycles on the Harish-Chandra Schwartz algebra of…

In this paper, we use $\mathcal D$-split sequences and derived equivalences to provide formulas for calculation of higher algebraic $K$-groups (or mod-$p$ $K$-groups) of certain matrix subrings which cover tiled orders, rings related to…

We give the graded Cartan determinants of the symmetric groups. Based on it, we propose a gradation of Hill's conjecture which is equivalent to K\"ulshammer-Olsson-Robinson's conjecture on the generalized Cartan invariants of the symmetric…

We compute the class of the classifying stack of the exceptional algebraic group $G_2$ and of the spin groups $\mathrm{Spin}_7$ and $\mathrm{Spin}_8$ in the Grothendieck ring of stacks, and show that they are equal to the inverse of the…

Let $\gamma$ denote imaginary parts of complex zeros of the Riemann zeta-function $\zeta(s)$. Certain sums over the $\gamma$'s are evaluated, by using the function $G(s) = \sum_{\gamma>0}\gamma^{-s}$ and other techniques. Some integrals…

Let mathcal{O}_lambda be a generic coadjoint orbit of a compact semi-simple Lie group K. Weight varieties are the symplectic reductions of mathcal{O}_lambda by the maximal torus T in K. We use a theorem of Tolman and Weitsman to compute the…

A homology class $d \in H_2(X)$ of a complex flag variety $X = G/P$ is called a line degree if the moduli space $\overline{M}_{0,0}(X,d)$ of 0-pointed stable maps to $X$ of degree $d$ is also a flag variety $G/P'$. We prove a quantum equals…

Spin polarization of the "second generation" nu_e=4/11 fractional quantum Hall state (corresponding to an incompressible liquid in a one-third-filled composite fermion Landau level) is studied by exact diagonalization. Spin phase diagram is…

We propose a method for computing generating functions of genus-zero invariants of a gauged linear sigma model $(V, G, \theta, w)$. We show that certain derivatives of $I$-functions of quasimap invariants of $[V //_\theta G]$ produce…

Let $G$ be a compact Lie group, $H$ a closed subgroup of maximal rank and $X$ a topological $G$-space. We obtain a variety of results concerning the structure of the $H$-equivariant K-ring $K_H^*(X)$ viewed as a module over the…