相关论文: Multivariate Lag-Windows and Group Representations
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
We present here the K-theoretic version of mirror models of toric manifold. First, we recall the construction of cohomological mirrors for toric manifolds, i.e. representations of the toric hypergeometric functions from quantum cohomology…
Outlined in this paper is a description of \emph{equivariance} in the world of 2-dimensional extended topological quantum field theories, under a topological action of compactLie groups. In physics language, I am gauging the theories ---…
The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…
A crucial role in representation theory of loop groups of reductive Lie groups and their Lie algebras is played by their non-trivial second cohomology classes which give rise to their central extensions (the affine Kac-Moody groups and Lie…
Tracking non-stationary covariance matrices is fundamental to vision yet hindered by existing estimators that either neglect manifold constraints or rely on first-order updates, incurring inevitable phase lag during rapid evolution. We…
Copula-based time series models can model univariate and stationary time series in a flexible way by decomposing the joint distribution of consecutive observations into a copula and the stationary distribution. Implicitly this approach…
In this paper we make a clear relationship between the automorphic representations and the quantization through the Geometric Langlands Correspondence. We observe that the discrete series representation are realized in the sum of…
Let G be a Lie group, $T^*G$ its cotangent bundle with its natural Lie group structure obtained by performing a left trivialization of T^*G and endowing the resulting trivial bundle with the semi-direct product, using the coadjoint action…
Every locally normal representation of a local chiral conformal quantum theory is covariant with respect to global conformal transformations, if this theory is diffeomorphism covariant in its vacuum representation. The unitary, strongly…
We consider the example from invariant theory concerning the conjugation action of the general linear group on several copies of the $n \times n$ matrices, and examine a symmetric function which stably describes the Hilbert series for the…
In the last few years, the notion of symmetry has provided a powerful and essential lens to view several optimization or sampling problems that arise in areas such as theoretical computer science, statistics, machine learning, quantum…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…
In this paper, we study extra-twists for automorphic representations of $\mathrm{GL}_n$ and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic…
We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of \v{S}penko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves…