8th Croatian Mathematical Congress

Session

Representation theory

RT

5 Jul 2024, 10:30

D8 (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

Conveners

Representation theory

• Darija Brajkovic Zoric (School of Applied Mathematics and Informatics, Josip Juraj Strossmayer University of Osijek)

131. Aubert involution on the unitary dual of SO(7) supported on the minimal parabolic subgroup

Dr Darija Brajkovic Zoric (School of Applied Mathematics and Informatics, Josip Juraj Strossmayer University of Osijek)

05/07/2024, 10:30

RT: Representation theory

Talk

There is the conjecture stating that the Aubert involution preserves unitarity. After finding the unitary dual of $p$-adic group $SO(7)$ with support on minimal parabolic subgroup, we found it intriguing to look at all the Aubert duals of all irreducible unitarizable subquotients that form that unitary dual. In doing that we confirmed the aforementioned conjecture for this case. This work is...

99. Induced representations of $p$-adic classical groups in the case of two segments and one half cuspidal reducibility

Igor Ciganović (University of Zagreb, Faculty of Science)

05/07/2024, 10:50

RT: Representation theory

Talk

We consider composition series of representations of a classical group over p-adic field, induced from two irreducible representations of GL, attached to a certain class of segments, and a cuspidal representation of a smaller classical group, where cuspidal reducibility is one half.

111. On the calculation of the inverse of the Varchenko matrix of the oriented braid arrangement

Milena Sošić (Faculty of Mathematics, University of Rijeka)

05/07/2024, 11:10

RT: Representation theory

Talk

We start with the basic notions of a hyperplane arrangement on $\mathbb{R}^n$ and then explain the braid arrangement on $\mathbb{R}^n$, which consists of $\frac{n(n-1)}{2}$ hyperplanes $H_{ij}=\{(x_1,x_2,\dots, x_n)\in \mathbb{R}^n\mid x_i=x_j\}$, $1\le i < j\le n$. Each region $P_\sigma$ of this arrangement is in one-to-one correspondence with a permutation $\sigma$ as follows...

71. Realizations of the Extended Snyder model

Tea Martinić Bilać (Faculty of Science, University of Split)

05/07/2024, 11:30

RT: Representation theory

Talk

We present the exact realization of the extended Snyder model.
Using similarity transformations we construct realizations of the original Snyder and the extended Snyder models.
Finally, we present the exact new realization of the $\kappa$–deformed extended Snyder model.