Related papers: Schur analysis and discrete analytic functions: Ra…
A series of bilinear identities on the Schur symmetric functions is obtained with the use of Pluecker relations.
We use hook Schur functions to compute trace cocharacters of matrices in hooks. As an example we compute the cocharacters of 3 x 3 matrices in the one by two hook.
The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field of analytic combinatorics in several…
We characterize the $k$-Schur functions as the graded characters of simple objects in an additive module category. This confirms a set of conjectures formulated in the Ph.D. thesis of Chen, written under the direction of Mark Haiman, and…
Taylor expansions of analytic functions are considered with respect to two points. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these…
In the context of the complex-analytic structure within the open unit disk, that was established in a previous paper, here we establish a simple generalization of the Cauchy-Goursat theorem of complex analytic functions. We do this first…
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is…
We provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood--Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur…
The notion of constructible functions in the setting of tame real geometry has been introduced by Cluckers and Dan Miller in their work on parametric integration of globally subanalytic functions. A function on a globally subanalytic set is…
In this second article of the series we study holomorphic families of generic rational matrix functions parameterized by the pole and zero loci. In particular, the isoprincipal deformations of generic rational matrix functions are proved to…
We classify the $Q$-multiplicity-free skew Schur $Q$-functions. Towards this result, we also provide new relations between the shifted Littlewood-Richardson coefficients.
We derive several identities involving Ikeda and Naruse's $K$-theoretic Schur $P$- and $Q$-functions. Our main result is a formula conjectured by Lewis and the second author which expands each $K$-theoretic Schur $Q$-function in terms of…
We provide necessary and sufficient conditions for operator-valued functions on arbitrary sets associated with a collection of test functions to have factorizations in several situations.
We prove that the Schweitzer complex is elliptic and its cohomologies define cohomological functors. As applications, we obtain finite dimensionality, a version of Serre duality, restrictions of the behaviour of cohomology in small…
Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…
We develop a cohomology theory of groups based on partial actions and explore its relation with the partial Schur multiplier as well as with cohomology of inverse semigroups.
We extend the work of A. Ciaffaglione and P. Di Gianantonio on mechanical verification of algorithms for exact computation on real numbers, using infinite streams of digits implemented as co-inductive types. Four aspects are studied: the…
A Lie theoretic interpretation is given for some formulas of Schur functions and Schur $Q$-functions. Two realizations of the basic representation of the Lie algebra $A^{(2)}_2$ are considered; one is on the fermionic Fock space and the…
The summation arithmetic functions with asymptotically independent summands are studied in the paper. We prove statements about the condition under which the summation arithmetic functions have asymptotically independent summands. It is…
Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations…