BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alfons Van Daele (KU Leuven\, Belgium) DTSTART:20221115T150000Z DTEND:20221115T160000Z DTSTAMP:20260422T180214Z UID:QGS/67 DESCRIPTION:Title: Alg ebraic quantum hypergroups and duality\nby Alfons Van Daele (KU Leuven \, Belgium) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nLet $G$ be a finite group and $H$ a subgroup. The set $\\mathcal{G}$ of double co sets $HpH$\, with $p \\in G$ has the structure of an hypergroup. The produ ct of two elements $HpH$ and $HqH$ is the set of cosets $HrH$ where $r \\i n pHq$. The algebra $A$ of functions on $\\mathcal{G}$ is the space of fun ctions on $G$ that are constant on double cosets. It carries a natural cop roduct\, dual to the product\, and given by\n$$∆(p\,q) = \\frac{1}{n} \\ sum_{h \\in H} f(phq)$$\nwhere $n$ is the number of elements in $H$. The d ual algebra is known as the Hecke algebra associated with the pair $G\,H$. \nIn this talk I will discuss the notion of an algebraic quantum hypergrou p\, its fundamental properties and duality for algebraic quantum hypergrou ps.\nI will illustrate this with an example\, coming from bicrossproduct t heory\, constructed from a pair of closed subgroups $H$ and $K$ of a group $G$\, with the assumption that $H \\cap K = {e}$.\nThis is part of more g eneral work in progress with M. Landstad (NTNU\, Trondheim)\n LOCATION:https://researchseminars.org/talk/QGS/67/ END:VEVENT END:VCALENDAR