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Vít Tuček

Publications and source records attributed to Vít Tuček.

7 recordsLinked to original sources

Large Language Models as Implicit Sociological Models: Reconstructing Voting Behaviour from Sociodemographic Profiles

Large language models (LLMs) trained on large-scale internet corpora encode extensive statistical regularities about social identities, attitudes, and political behaviour. This paper introduces and evaluates a methodological framework that leverages these latent representations to reconstruct aggregate voting behaviour from individual-level sociodemographic profiles. We operationalize LLMs as implicit sociological models by conditioning them on demographic descriptions, eliciting probabilistic turnout and party preferences, and aggregating individual outputs via a soft voting procedure. Using the 2021 Czech parliamentary election as a validation case, we demonstrate that contemporary LLMs reproduce official election outcomes with low mean absolute error, recover known political bloc structures, and align with independently established sociodemographic gradients. The contribution of this work is methodological rather than predictive: we show how LLMs can be systematically interrogated as compressed representations of social reality, offering a novel exploratory instrument for computational social science while clearly delineating its epistemic and ethical limits.

cs.CY↗

Unitary highest weight modules for $\mathfrak{su}(p, q)$ and $\mathfrak{so}^{*}(2n)$ with fixed integral infinitesimal character

We classify unitary highest weight modules with a given integral infinitesimal character for the real Lie algebras $\mathfrak{su}(p,q)$ and $\mathfrak{so}^*(2n)$. We treat both regular and singular cases. For $\mathfrak{su}(p,q)$ we identify the unitarizable modules in the Hasse diagrams of the highest weight orbit. Analogous results for the other Hermitian Lie algebras were given in our earlier publications.

math.RT↗

On the classification of unitary highest weight modules in the exceptional cases

In our previous paper, we gave a complete classification of the unitary highest weight modules for the universal covers of the Lie groups $Sp(2n, \mathbb{R}), SO^{*}(2n)$ and $SU(p, q)$, using the Dirac inequality and the so called PRV product. In this paper, we complete the classification of the unitary highest weight modules for the remaining cases; i.e., universal covers of the Lie groups $SO_{e}(2, n)$, $E_{6(-14)}$ and $E_{7(-25)}$. We also describe unitary highest weight modules with given infinitesimal characters.

math.RT↗

On the classification of unitary highest weight modules

In the 1980s, Enright, Howe and Wallach [EHW] and independently Jakobsen [J] gave a complete classification of the unitary highest weight modules. In this paper we give a more direct and elementary proof of the same result for the (universal covers of the) Lie groups $Sp(2n, \mathbb{R}), SO^{*}(2n)$ and $SU(p, q)$. We also show how to describe the set of unitary highest weight modules with a given infinitesimal character.

math.RT↗

Dirac inequality for highest weight Harish-Chandra modules I

Let $G$ be a connected simply connected noncompact classical simple Lie group of Hermitian type. Then $G$ has unitary highest weight representations. The proof of the classification of unitary highest weight representations of $G$ given by Enright, Howe and Wallach is based on the Dirac inequality of Parthasarathy, Jantzen's formula and Howe's theory of dual pairs where one group in the pair is compact. In this paper we focus on the Dirac inequality which can be used to prove the classification in a more direct way.

math.RT↗

Hyperplane section $\mathbb{OP}^2_0$ of the complex Cayley plane as the homogeneous space $\mathrm{F_4/P_4}$

We prove that the exceptional complex Lie group $F_4$ has a transitive action on the hyperplane section of the complex Cayley plane $\mathbb{OP}^2$. Our proof is direct and constructive. We use an explicit realization of the vector and spin actions of $\Spin(9,\C) \leq F_4$. Moreover, we identify the stabilizer of the $F_4$-action as a parabolic subgroup $P_4$ (with Levi factor $B_3T_1$) of the complex Lie group $F_4$. In the real case we obtain an analogous realization of $F_4^{(-20)}/P_4$.

math.AG↗