SMS scnews item created by Ruibin Zhang at Fri 28 Nov 2014 1220
Type: Seminar
Distribution: World
Expiry: 2 Dec 2014
Calendar1: 2 Dec 2014 1205-1300
CalLoc1: AGR Carslaw 829
CalTitle1: Algebra Seminar: Peter D Jarvis, University of Tasmania -- Ribbon Hopf algebras from group character rings
Auth: rzhang(.pmstaff;2417.2002)@p722.pc.maths.usyd.edu.au

# Algebra Seminar: Peter D Jarvis -- Ribbon Hopf algebras from group character rings

Ribbon Hopf algebras from group character rings

Peter Jarvis
School of Physical Sciences
University of Tasmania

Joint work with Bertfried Fauser and Ronald King

We study the diagram alphabet of knot moves associated with the character
rings of certain matrix groups. The primary object is the Hopf algebra
of characters of the finite dimensional polynomial representations of
the complex group $GL(n)$ in the inductive limit, realised as the ring of
symmetric functions $\Lambda(X)$ on countably many variables, as well as
the formal character rings of algebraic subgroups of $GL(n)$, comprised of
matrix transformations leaving invariant a fixed but arbitrary tensor of
Young symmetry type $\pi$, which include the orthogonal and symplectic groups
as special cases. From these elements we assemble for each $\pi$ a crossing tangle
which satisfies the braid relation and which is nontrivial, in spite of
the commutative and co-commutative setting. We identify structural
elements and verify the axioms to establish that each Char-H$_\pi$ ring
is a ribbon Hopf algebra. The corresponding knot invariant operators are
rather weak, giving merely a measure of the writhe.


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