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thank you first Id like to thank the organizers for the invitation its a its a pleasure to be here so I will speak about an ongoing project with the initial seed or and I like to start with motivations so in fact it is a motivation that we already seen in a bizarre stock so its a so-called refined GDP conjecture about unitary groups so let me recall the further setting so we start from a quadratic extension of the number field and we denote Sigma as a generator of the Galois group and we start with e deco space of fatigue dimension and equipped with nondegenerate emission sigma emission form and we extend this space by adding a line and we extend the form so that so some air is orthogonal and we normalize we normalize the added vector in the following way so with this data we can attach first a unitary group did 13 by H so this is unitary group attached to V and we have the unitary group of V times the unitary group of the value and it will be denoted by by G and we have a diagona
