Related papers: D\'{e}vissage Hermitian Theory

We compute the additive structure of the Hermitian $K$-theory spectrum of an even-dimensional Grassmannian over a base field $k$ of characteristic zero in terms of the Hermitian $K$-theory of $X$, using certain symmetries on Young diagrams.…

Let $k$ be an algebraically closed field of characteristic $p > 0$ and let $G$ be a connected reductive algebraic group over $k$. Under some standard hypothesis on $G$, we give a direct approach to the finite $W$-algebra $U(\mathfrak g,e)$…

Grothendieck-Witt spectra represent higher Grothendieck-Witt groups and higher Hermitian K-theory in particular. A description of the Grothendieck-Witt spectrum of a finite dimensional projective bundle $\mathbb{P}(\mathcal{E})$ over a base…

Dijkgraaf-Witten theories are quantum field theories based on (form degree 1) gauge fields valued in finite groups. We describe their generalization based on $p$-form gauge fields valued in finite abelian groups, as field theories extended…

We prove a reduced version of the Chevalley restriction conjecture on the commuting scheme posed by T.H. Chen and B.C. Ng\^o, extending the results of Hunziker for classical groups. In particular, we prove that for any connected reductive…

For G a complex reductive group and X a smooth projective or convex quasi-projective polarized G-variety we construct a formal map in quantum K-theory from the equivariant quantum K-theory $QK^G(X)$ to the quantum K-theory of the git…

Let X be a noetherian scheme of finite Krull dimension, having 2 invertible in its ring of regular functions, an ample family of line bundles, and a global bound on the virtual mod-2 cohomological dimensions of its residue fields. We prove…

The question of whether the group $\mathbb{Q}_p \rtimes \mathbb{Q}_p^*$ is Hermitian has been stated as an open question in multiple sources in the literature, even as recently as a paper by R. Palma published in 2015. In this note we…

We consider $N\times N$ symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove…

The Grothendieck-Serre conjecture predicts that every generically trivial torsor under a reductive group $G$ over a regular semilocal ring $R$ is trivial. We establish this for unramified $R$ granted that $G^{\mathrm{ad}}$ is totally…

Let G be a group and let W be an algebra over a field K. We will say that W is a G-graded twisted algebra if W can be written as a direct sum over the elements of G of one dimensional K-vector spaces. It is also assumed that W has no…

We study the algebra of Wilson line operators in three-dimensional N=2 supersymmetric U(M) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M,N), and its connection to K-theoretic Gromov-Witten invariants for Gr(M,N).…

In 2005 J.L. Waldspurger proved the following theorem: given a finite real reflection group $W$, the closed positive root cone is tiled by the images of the open weight cone under the action of the linear transformations $id-w$. Shortly…

Let $T$ be a compact torus and $(M,\omega)$ a Hamiltonian $T$-space. We give a new proof of the $K$-theoretic analogue of the Kirwan surjectivity theorem in symplectic geometry by using the equivariant version of the Kirwan map introduced…

For a finite abelian group $G$ and a splitting field $K$ of $G$, let $d(G, K)$ denote the largest integer $l \in \N$ for which there is a sequence $S = g_1 \cdot ... \cdot g_l$ over $G$ such that $(X^{g_1} - a_1) \cdot ... \cdot (X^{g_l} -…

We propose a generalization of Haiman's conjecture on the diagonal coinvariant rings of real reflection groups to the context of irreducible quaternionic reflection groups (also known as symplectic reflection groups). For a reflection group…

We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. We also identify the homotopy fibers of the…

We prove the following theorem. Let $G$ be a finite group generated by unitary reflections in a complex Hermitian space $V=\mathbb{C}^\ell$ and let $G'$ be any reflection subgroup of $G$. Let $\mathcal{H}(G)$ be the space of $G$-harmonic…

We prove general results about completeness of cotorsion theories and existence of covers and envelopes in locally presentable abelian categories, extending the well-established theory for module categories and Grothendieck categories.…

We exhibit a canonical equivalence between the hermitian $K$-theory (alias Grothendieck-Witt) spectrum of an exact form category and that of its derived Poincar\'e $\infty$-category, with no assumptions on the invertibility of $2$. Along…