相关论文: Mislin's theorem for fusion systems via Mackey fun…

In this paper, we prove a new generalized Mikhlin multiplier theorem whose conditions are given with respect to fractional derivatives in integral forms with two different integration intervals. We also discuss the connection between…

We give a new proof of quantum Shannon-McMillan theorem, extending it to AF $C^*$-systems. Our proof is based on the variational principle, instead of the classical Shannon-McMillan theorem.

The Mishchenko-Fomenko theorem on superintegrable Hamiltonian systems is generalized to superintegrable Hamiltonian systems with noncompact invariant submanifolds. It is formulated in the case of globally superintegrable Hamiltonian systems…

We study here the higher derived limits of mod $p$ cohomology on the centric orbit category of a saturated fusion system on a finite $p$-group. It is an open problem whether all such higher limits vanish. This is known in many cases,…

We say that a fusion system is the composition product of two subsystems if every morphism can be factored as a morphism in one fusion system followed by a morphism in the other. We establish a relationship between the characteristic…

We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…

We build a spectral sequence converging to the cohomology of a fusion system with a strongly closed subgroup. This spectral sequence is related to the Lyndon-Hochschild-Serre spectral sequence and coincides with it for the case of an…

We relate the construction of groups which realize saturated fusion systems and signaliser functors with homology decompositions of p-local finite groups. We prove that the cohomology ring of Robinson's construction is in some precise sense…

We settle the fusion product decomposition theorem for higher-level affine Demazure modules for the cases $E^{(1)}_{6, 7, 8}, F^{(1)}_4$ and $E^{(2)}_{6}$, thus completing the main theorems of Chari et al. (J. Algebra, 2016) and Kus et al.…

We enlarge the category of bornological coarse spaces by adding transfer morphisms and introduce the notion of an equivariant coarse homology theory with transfers. We then show that equivariant coarse algebraic $K$-homology and equivariant…

We prove that the space of intertwining operators associated with certain admissible modules over vertex operator algebras is isomorphic to a quotient of the vector space of conformal blocks on a three-pointed rational curve defined by the…

The Mishchenko-Fomenko theorem on noncommutative integrability of Hamiltonian systems on a symplectic manifold is extended to the case of noncompact invariant submanifolds.

We give a new proof of a formula for the fusion rules for type $A_2$ due to B\'egin, Mathieu, and Walton. Our approach is to symbolically evaluate the Kac-Walton algorithm.

We develop tools which use common fusion systems building techniques in order to compute higher limits over the centric orbit category. We apply these tools in order to study both the Diaz-Park sharpness conjecture as well as the weaker…

Viewing group cohomology as a cohomological functor, G. Mislin has generalised Tate cohomology from finite groups to all discrete groups by defining a completion for cohomological functors in 1994. In a previous paper, we have constructed…

We study the D\'iaz-Park sharpness conjecture for fusion systems and prove that, under certain circumstances, there exists a 4 terms exact sequence relating the first two higher limits of the contravariant part of a Mackey functor over…

We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency…

We discuss a recent proof by the author of a general version of the Verlinde conjecture in the framework of vertex operator algebras and the application of this result to the construction of modular tensor tensor category structure on the…

In this paper, we construct a restriction morphism on the critical cohomology of an equivariant Landau-Ginzburg model associated to a representation of a reductive group equipped with an invariant function. We show a compatibility formula…

We develop tools to prove D\'iaz and Park's sharpness conjecture (see [8]) for fusion systems admitting tame families of fusion subsystems (see Theorem A). We use such tools to prove the conjecture for all Benson-Solomon fusion systems (see…