Related papers: Hua type integrals over unitary groups and over pr…

We construct $p$-adic counterparts of Hua measures, measures on inverse limits of $p$-adic Grassmannians, and describe natural groups of symmetries of such measures.

We construct a family of measures on flag spaces (or, equivalently, on the spaces of upper-triangular matrices) compatible with respect to natural projections. We obtain an $n(n-1)/2$-parametric family of beta-integrals over space of…

Consider the space $C$ of conjugacy classes of a unitary group $U(n+m)$ with respect to a smaller unitary group $U(m)$. It is known that for any element of the space $C$ we can assign canonically a matrix-valued rational function on the…

We revisit the work of the first named author and using simpler algebraic arguments we calculate integrals of polynomial functions with respect to the Haar measure on the unitary group U(d). The previous result provided exact formulas only…

We adopt the concept of the composite parameterization of the unitary group U(d) to the special unitary group SU(d). Furthermore, we also consider the Haar measure in terms of the introduced parameters. We show that the well-defined…

In this article, we study integrals on the unitary group with respect to the Haar measure. We give a combinatorial interpretation in terms of maps of the asymptotic topological expansion, established previously by Guionnet and Novak. The…

Integrals for the product of unitary-matrix elements over the U(n) group will be discussed. A group-theoretical formula is available to convert them into a multiple sum, but unfortunately the sums are often tedious to compute. In this…

Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…

We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.

We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of…

We generalise well-known integrals of Ingham-Siegel and Fisher-Hartwig type over the unitary group $U(N)$ with respect to Haar measure, for finite $N$ and including fixed external matrices. When depending only on the eigenvalues of the…

We consider integrals of type $\int_{O_n}u_{11}^{a_1}... u_{1n}^{a_n}u_{21}^{b_1}... u_{2n}^{b_n} du$, with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such…

We characterize all translation invariant half planar maps satisfying a certain natural domain Markov property. For p-angulations with p \ge 3 where all faces are simple, we show that these form a one-parameter family of measures…

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…

We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one can reduce the matrix integral to the…

We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one…

We evaluated some particular type of functional integral over the local gauge group C^{\infty}({\bf R}^n, U(1)) by going to a discretized lattice. The results explicitly violates the property of the Haar measure. We also analysed the…

We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of…

Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they…

We find new representations for Itzykson-Zuber like angular integrals for arbitrary beta, in particular for the orthogonal group O(n), the unitary group U(n) and the symplectic group Sp(2n). We rewrite the Haar measure integral, as a flat…