English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In the recent paper [arXiv:1109.1412], Borodin and Olshanski have presented a novel proof of the celebrated Edrei-Voiculescu theorem which describes the boundary of the Gelfand-Tsetlin graph as a region in an infinite-dimensional coordinate space. This graph encodes branching of irreducible characters of finite-dimensional unitary groups. Points of the boundary of the Gelfand-Tsetlin graph can be identified with finite indecomposable (= extreme) characters of the infinite-dimensional unitary group. An equivalent description identifies the boundary with the set of doubly infinite totally nonnegative sequences. A principal ingredient of Borodin-Olshanski's proof is a new explicit determinantal formula for the number of semi-standard Young tableaux of a given skew shape (or of Gelfand-Tsetlin schemes of trapezoidal shape). We present a simpler and more direct derivation of that formula using the Cauchy-Binet summation involving the inverse Vandermonde matrix. We also obtain a q-generalization of that formula, namely, a new explicit determinantal formula for arbitrary q-specializations of skew Schur polynomials. Its particular case is related to the q-Gelfand-Tsetlin graph and q-Toeplitz matrices introduced and studied by Gorin [arXiv:1011.1769].

The Boundary of the Gelfand–Tsetlin Graph: New Proof of Borodin–Olshanski’s Formula, and its q-Analogue