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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present in this paper the algebra of fused permutations and itsdeformation the fused Hecke algebra. The first one is defined on a set ofcombinatorial objects that we call fused permutations, and its deformation isdefined on a set of topological objects that we call fused braids. We use thesealgebras to prove a Schur--Weyl duality theorem for any tensor products of anysymmetrised powers of the natural representation of $U_q(gl_N)$. Then weproceed to the study of the fused Hecke algebras and in particular, we describeexplicitely the irreducible representations and the branching rules. Finally,we aim to an algebraic description of the centralisers of the tensor productsof $U_q(gl_N)$-representations under consideration. We exhibit a simpleexplicit element that we conjecture to generate the kernel from the fused Heckealgebra to the centraliser. We prove this conjecture in some cases and inparticular, we obtain a description of the centraliser of any tensor productsof any finite-dimensional representations of $U_q(sl_2)$.

Fused braids and centralisers of tensor representations of $U_q(gl_N)$