A HOPF ALGEBRA ON DOUBLE POSETS WITH A LITTLEWOOD-RICHARDSON RULE
speaker: Claudia Malvenuto (Dipartimento di Matematica Sapienza Università di Roma )abstract: We define a combinatorial Hopf algebra based on double posets, endowed with a symmetric bilinear form based on pictures between double posets, in analogy to pictures of tableaux as defined by Zelevinsky , extending straightforwardly to double posets. This form is a Hopf pairing on the previous Hopf algebra. Thus we obtain a link between two articles of Zelevinsky: the one mentioned above and the contemporary article, where he studied self-dual Hopf algebras arising from the character theory of classical finite groups. The results we prove show that pictures are fundamentally linked to scalar products, a point of view already present in Zelevinsky’s work, who proved that the scalar product of two skew Schur functions is equal to the number of pictures between their shapes.
timetable:
Thu 11 Apr, 9:30 - 10:30, Sala Conferenze Centro De Giorgi
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