Related papers: Semi-Orthogonal Decompositions for Rank Two Imprim…

Let BP be the p-completed classifying space of a p-group P with p-rank 2. For an odd prime p, by using stable homotopy splitting of BP, we study the decomposition of even dimensional parts of the integral cohomology and the Chow ring of BP.

We compute the arithmetic rank as well as the local/\'etale cohomological dimension of nullcone ideals arising from the classical actions of the symplectic group, the general linear group, and the orthogonal group. We use these calculations…

We show that every countable set of partial bijections from an infinite set to itself can be obtained as a composition of just two such partial bijections. This strengthens a result by Higgins, Howie, Mitchell and Ru\v{s}kuc stating that…

Given a split simply connected and connected algebraic group scheme $\mathbb G$ over $\mathbb Z$ and a split parabolic subgroup scheme $\mathbb P\subset \mathbb G$, this paper constructs semi-orthogonal decompositions of the bounded derived…

There are 432 strongly squarefree symmetric bilinear forms of signature $(2,1)$ defined over $\Z[\sqrt{2}]$ whose integral isometry groups are generated up to finite index by finitely many reflections. We adapted Allcock's method (based on…

In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic k-rank of complex-valued forms of any degree divisible by k…

We classify the bireflections (products of 2 involutions) in the commutator subgroup G an orthogonal group O(V) over a finite field GF(q) of characteristic not 2. We show that every element of G is a bireflection if it is reversible…

We study topologization of the semigroup $\mathscr{O\!\!I}\!_n(L)$ of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set $(L,\leqslant)$. In particular we show that every $T_1$ left-topological…

This article constructs Von Neumann invariants for constructible complexes and coherent D-modules on compact complex manifolds, generalizing the work of the author on coherent L 2-cohomology. We formulate a conjectural generalization of…

We prove the first nontrivial reconstruction theorem for modular tensor categories: the category associated to any twisted Drinfeld double of any finite group, can be realised as the representation category of a completely rational…

Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…

All exactly integrable systems connected with the semisimple algebras of the second rank with an arbitrary choice of the grading in them are presented in explicit form. General solution of such systems are expressed in terms of the matrix…

The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.

We give a complete classification (up to isomorphism) of Lie conformal algebras which are free of rank two as $\C[\partial]$-modules, and determine their automorphism groups.

We study the multiplicative structure of orbifold Hochschild cohomology in an attempt to generalize the results of Kontsevich and Calaque-Van den Bergh relating the Hochschild and polyvector field cohomology rings of a smooth variety. We…

We prove that the equivariant derived category for a finite subgroup of GL(3,C) has a semi-orthogonal decomposition into the derived category of a certain partial resolution, called a maximal Q-factorial terminalization, of the…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

The theory of spectral methods for partial differential equations leads to infinite-dimensional matrices which represent the derivative operator with respect to an underlying orthonormal basis. Favourable properties of such differentiation…

We prove a relative version of the fact that semiorthogonal decompositions of the bounded derived category of coherent sheaves are strongly constrained by the base locus of the canonical linear system. As an application we prove that the…

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case…