Discrete mathematical modelling seminar

Seminar information archive ~06/09Next seminarFuture seminars 06/10~

Organizer(s) Tetsuji Tokihiro, Ralph Willox


17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Adam Doliwa (University of Warmia and Mazury)
The Hopf algebra structure of coloured non-commutative symmetric functions
[ Abstract ]
The Hopf algebra of symmetric functions (Sym), especially its Schur function basis, plays an important role in the theory of KP hierarchy. The Hopf algebra of non-commutative symmetric functions (NSym) was introduced by Gelfand, Krob, Lascoux, Leclerc, Retakh and Thibon. In my talk I would like to present its "A-coloured" version NSym_A and its graded dual - the Hopf algebra QSym_A of coloured quasi-symmetric functions. It turns out that these two algebras are both non-commutative and non-cocommutative (for |A|>1), and their product and coproduct operations allow for simple combinatorial meaning. I will also show how the structure of the poset of sentences over alphabet A (A-coloured compositions) gives rise to a description of the corresponding coloured version of the ribbon Schur basis of NSym_A.