Letters in Mathematical Physics最新文献

In this paper, we use Schur elements to derive semisimplicity criteria for (super) symmetric superalgebras. We obtain a closed formula for the Schur elements of cyclotomic Hecke–Clifford superalgebras (mathcal {H}^{f}_{mathbb {K}}). As applications, we prove that two trace functions (gimel _n) and (t_{1,n}) on the Hecke–Clifford superalgebra, which are defined in different ways, are proportional. We give a semisimplicity criterion for (mathcal {H}^{f}_{mathbb {K}}) when it is (super)symmetric. We also derive semisimplicity criteria for cyclotomic quiver Hecke superalgebras of types (A^{(1)}_{e}), (C^{(1)}_{e}), (A^{(2)}_{2e}) and (D^{(2)}_{e+1}).

Following [3], we analyze the long-time asymptotics of the autocorrelation function of the transverse Ising chain at the critical magnetic field (a special case of the spin-(frac{1}{2}) XY model in a magnetic field) via the associated Riemann–Hilbert problem. We refine the original Deift–Zhou’s result by determining the subleading growing term in the asymptotics.

In this paper, we establish a series of rigidity results for initial data sets with boundary in the presence of marginally outer trapped surfaces (MOTSs) satisfying a capillary boundary condition. Our first result establishes area estimates for stable MOTS with capillary boundary. Building on this, we prove a rigidity theorem for three-dimensional initial data sets with boundary. We further extend the rigidity to higher dimensions by employing the Yamabe constant associated to the MOTS. Finally, under a low-index assumption, we obtain additional topological restrictions on MOTS with capillary boundary.

The goal of this note is to show that the standard BV formulation of gravity in the Palatini–Cartan formalism is equivalent, using a BV pushforward, to an AKSZ-like version compatible with BFV data on the boundary.

In this paper, we define a Grothendieck ring as a fusion ring categorifiable into a fusion category over the complex field. An integral fusion ring is called Drinfeld if all its formal codegrees are integers dividing the global Frobenius–Perron dimension. Every integral Grothendieck ring is necessarily Drinfeld. Using the fact that the formal codegrees of integral Drinfeld rings form an Egyptian fraction summing to 1, we derive a finite list of candidate global FPdims for small ranks, covering all that occur. Using Normaliz (an open-source software for computing algebraic polyhedra), we classify all integral fusion rings with these candidate FPdims, retaining only those admitting a Drinfeld structure. To exclude Drinfeld rings that are not Grothendieck rings, we analyze induction matrices to the Drinfeld center, classified via our new feature on Normaliz. Further exclusions and constructions involve group-theoretical fusion categories and Schur multipliers. Our main result is a complete classification of integral Grothendieck rings up to rank 5, extended to rank 7 in odd-dimensional and noncommutative cases using Frobenius–Schur indicators and Galois theory. Moreover, we show that any noncommutative, odd-dimensional, integral Grothendieck ring of rank at most 22 is pointed of rank 21. We also classify all integral 1-Frobenius Drinfeld rings of rank 6, identify the first known non-Isaacs integral fusion category (which turns out to be group-theoretical), and classify integral noncommutative Drinfeld rings of rank 8 and integral 1-Frobenius MNSD Drinfeld rings of rank 9. Finally, we determine the smallest rank simple exotic integral fusion rings: rank 4 in general, rank 6 in the Drinfeld case, and rank 7 in the 1-Frobenius Drinfeld case.

In this article we first introduce the notion of a 2-action of a Lie 2-algebra on an arbitrary manifold M. C.L. Rogers associates in [10] a (L_{infty })-algebra (mathsf {L^{infty }(M,omega )}) to a n-plectic manifold ((M,omega )), as a higher analogue of the Poisson algebra of observables associated to a symplectic manifold. This (L_{infty })-algebra reduces to a Lie 2-algebra (mathsf {L^2(M,omega )}) when ((M,omega )) is 2-plectic. Following ideas of N.L. Delgado (cf. [4]), we introduce the Lie 2-algebra (mathsf {D^2(M,omega )}), which generalises the Lie 2-algebra (textsf{L}^2(M,omega )), and its extension (mathsf {widetilde{D^2(M,omega )}}) containing Hamiltonian pairs. Given a 2-plectic manifold ((M,omega )) and a Lie 2-algebra (mathfrak {g}_{-1}oplus mathfrak {g}_{0}) acting on M we define a comomentum map as a lift of the action, i.e., as a Lie 2-algebra morphism from (mathfrak {g}_{-1}oplus mathfrak {g}_{0}) to the Lie 2-algebra (mathsf {widetilde{D^2(M,omega )}}). In an appendix, we discuss very explicitly numerous examples, classified according to their algebraic properties.

This paper initiates the study of invariants of links associated to infinite-dimensional representations of (U_q(mathfrak {sl}_2)) using graphical representation for quantum 6j-symbols, the shadow world. We obtain formulae for q3j-symbols and q6j-symbols for Verma modules and study their properties. This hints at the structure of a possible target category for Reshetikhin-Turaev functor for such an invariant.

We present a linear q-difference equation of rank 3, which admits the affine Weyl group symmetry of type (E_8^{(1)}). This equation has essentially 8 parameters and 2 accessory parameters. We characterize this equation by the spectral type of q-difference system which is introduced by Sakai–Yamaguchi. We further compare this equation with Moriyama–Yamada’s quantum curve which has (W(E_8^{(1)}))-symmetry. We show that our equation can be regarded as an extension of Moriyama–Yamada’s curve. We introduce the point configuration of a higher-order scalar q-difference equation to characterize our equation and clarify the corresponding between our equation and the curve. The symmetry of our equation is provided by the q-middle convolution, defined by Sakai–Yamaguchi and reformulated by Arai–Takemura. In this paper, we provide a reconstruction of the q-middle convolution via a q-Okubo-type equation. This construction is a natural q-analog of the middle convolution of Fuchsian differential equation. Several properties for our q-middle convolution are also discussed.

We construct the causal fermion system for globally hyperbolic spacetimes starting in the framework of algebraic quantum field theory. The fermionic projector is identified with the one-particle density operator of a quasi-free Hadamard state. The ultraviolet regularization is built into the fermionic projector via a chart-independent (ivarepsilon )-regularization scheme. The continuum limit analysis is developed in globally hyperbolic spacetimes. It is shown that the Euler–Lagrange equations of the causal action principle are satisfied in this setup if and only if the coupled Einstein–Dirac equations hold.