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Modality of representations and geometry of θ-groups
Ch. 16. P. 459–479.
We first establish several general properties of modality of algebraic group
actions. In particular,we introduce the notion of a modality-regular action and prove
that every visible action is modality-regular. Then, using these results, we classify irreducible
linear representations of connected simple algebraic groups of every fixed
modality < 3. Next, exploring a finer geometric structure of linear actions, we generalize
to the case of any cyclically graded semisimple Lie algebra the notion of a
packet (or a Jordan/decomposition class) and establish the properties of packets.
In book
Kac, V., Popov, Vladimir L. Vol. 326. , Copyright Holder Springer Nature Switzerland AG, 2018.
Prokofieva K., В кн.: Японский язык в вузе: актуальные проблемы преподавания. Сборник научных работ. Материалы Второго международного форума «Языки и культуры Восточной Азии в образовательном пространстве» (МГПУ, 23–26 апреля 2025). Выпуск 30Вып. 30: Сборник научных работ. Материалы Второго международного форума.: МГПУ, Языки народов мира, 2025. С. 325–333.
When teaching Japanese as a foreign language, it is customary to explain grammatical markers that convey the meanings of wish and invitation to joint action separately from each other. Meanwhile, comparing these markers for a more accurate understanding of the speaker's intentions, as well as the variability of the context of their use, can be ...
Added: April 26, 2026
Тискин Д. Б., М.: Издательская группа URSS, 2026.
Предлагаемая книга представляет собой введение в формальную семантику — раздел языкознания, в котором посредством построения математически строгих моделей исследуется, как предложения приобретают значение и способность передавать информацию в зависимости от своей структуры и значений составляющих их слов. Классические теоретические идеи Г. Фреге, Д. Льюиса, Д. Каплана и др. излагаются современным языком, а при разработке нотации акцент сделан на том, ...
Added: March 17, 2026
Ivan Arzhantsev, Roman Avdeev, Yulia Zaitseva, International Mathematics Research Notices 2026 Vol. 2026 No. 4 Article rnag007
We complete the classification of algebraic monoid structures on the affine 3-space. The result is based on a reduction of the general case to that of commutative monoids. We also study various algebraic properties of all monoids appearing in the classification. ...
Added: February 24, 2026
Popov V., Успехи математических наук 2025 Т. 80 № 3(483) С. 189–190
It is proved that for any positive integers d and c, the set of isomorphism classes of all d-dimensional reductive algebraic groups with exactly c connected components is finite. As a corollary, the set of isomorphism classes of all d-dimensional compact real Lie groups with exactly c connected components is proved to be finite. To ...
Added: December 16, 2025
Letuchiy A., Russian Linguistics 2025 Т. 49 № 2 Статья 2
The article discusses types of interpretation that Russian complex sentences with factive,implicative and interpretation verbs get under negation and modal operators. By default,the external negative and modal context affects only the main situation. However, one findsexceptions of this rule. We call ‘transparent readings’ those readings in which the exter-nal context affects semantically both the matrix ...
Added: November 5, 2025
Prokofieva K., В кн.: Японский язык в вузе: актуальные проблемы преподавания. Сборник научных работ. Материалы Первого международного форума «Языки и культуры Восточной Азии в образовательном пространстве» (МГПУ, 13–16 марта 2024 г.). Выпуск 28Вып. 28: Сборник научных работ. Материалы Первого международного форума.: Языки народов мира, 2025. С. 291–300.
The category of modality in Japanese language is still widely discussed. What is the essence of modality for native Japanese speakers? How can it be expressed in a Japanese sentence? These two questions are among current ones till nowadays. Despite the extensive theoretical base and the existing traditional description of modality in Japanese linguistics, significant ...
Added: July 4, 2025
Arzhantsev I., Izvestiya. Mathematics 2009 Vol. 73 No. 3 P. 437–453
We study open equivariant projective embeddings of homogeneous spaces such that the complement of the open orbit has codimension at least 2. We establish a criterion for the existence of such an embedding, prove that the set of isomorphism classes of such embeddings is finite, and give a construction of the embeddings in terms of ...
Added: June 13, 2025
Arzhantsev I., Sbornik Mathematics 2001 Vol. 192 No. 8 P. 1133–1138
Let G be a reductive algebraic group and let H be a reductive subgroup of G. The modality of a G-variety X is the largest number of the parameters in a continuous family of G-orbits in X. A precise formula for the maximum value of the modality over all affine embeddings of the homogeneous space ...
Added: June 13, 2025
Rudnev D., Borisova T. Y., Вестник Новосибирского государственного университета. Серия: История, филология 2022 Т. 22 № 2 С. 9 – 20
The aim of the article is to describe the system of means of expressing permission in the language of docu- ments of the 18th century. On the basis of linguistic material extracted from collections of published documents, pat- terns of expression of permission and their dynamics during the 18th century are revealed. In the time ...
Added: May 7, 2025
Сизикова Т. Э., Леонов С. В., Polikanova I., Сибирский психологический журнал 2025 № 95 С. 78–95
Addressing the psychophysiological correlates of reflection in the context of modern psychology based on the integrity paradigm is an urgent and promising area. We rely on the ideas of L.S. Vygotsky and the critical ontology of N. Hartmann, which allow us to analyze reflection using modal analysis and take into account the relationship between mental ...
Added: March 8, 2025
Zaitseva Y., Results in Mathematics 2024 Vol. 79 Article 249
We give a classification of noncommutative algebraic monoid structures on normal affine varieties such that the group of invertible elements of the monoid is connected, solvable, and has a one-dimensional unipotent radical. We describe the set of idempotents and the center of such a monoid and give a criterion for existence of the zero element. ...
Added: September 13, 2024
Roman Avdeev, Communications in Contemporary Mathematics 2024 Vol. 26 No. 6 Article 2350029
In this paper, we obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain one-parameter degenerations of the Lie algebras corresponding to such subgroups. As an application, we exhibit explicit algorithms for computing the set of spherical ...
Added: December 27, 2023
Gayfullin S., Chunaev D., Фундаментальная и прикладная математика 2023 Т. 24 № 4 С. 47–59
In this work we obtain sufficient conditions for a variety with a torus action of complexity one to have finite number of automorphism group orbits. ...
Added: December 2, 2023
van der Auwera J., Plungian V., Linguistic Typology 1998 Vol. 2 No. 1 P. 79–124
Added: November 12, 2023
Vladimir Plungian, Åkerman Sarkisian K., Scando-Slavica 2023 Т. 69 № 1 С. 3–24
The so-called acquisitive modality or actuality, describing a successful realization of an action, is a largely understudied type of modal values. It is of significant interest both from the viewpoint of its grammaticalization paths and of a wide and rich variety of its lexical expression. The article discusses one of the main representatives of this ...
Added: November 8, 2023
Kasenov D., Paramonova D., Krainova A., , in: Девятнадцатая конференция по типологии и грамматике для молодых исследователей: тезисы докладов.: СПб.: ИЛИ РАН, 2022. P. 185–187.
Added: October 24, 2023
Beldiev I., Results in Mathematics 2023 Vol. 78 No. 5 Article 192
We study induced additive actions on projective hypersurfaces, i.e. effective regular actions of the algebraic group G_a^m with an open orbit that can be extended to a regular action on the ambient projective space. We prove that if a projective hypersurface admits an induced additive action, then it is unique if and only if the hypersurface is ...
Added: August 7, 2023
М.: Институт славяноведения РАН, 2023.
Определенность / неопределенность — одна из важнейших для балканского языкового союза и модели мира семантических категорий. Эксплицитно или имплицитно она проявляется на разных уровнях языка и во всех текстах, включая фольклор, обрядность, литературу и изобразительное искусство. В сборнике представлены материалы по темам: определенность / неопределенность в синхронии и диахронии языков и диалектов балканского языкового союза; ...
Added: April 3, 2023
Vladimir L. Popov, / Series math "arxiv.org". 2023. No. 2302.13374.
We prove that the Picard group of a connected affine algebraic group $G$ is isomorphic to the fundamental group of the derived subgroup of the reductive algebraic group $G/{\mathscr R}_u(G)$, where ${\mathscr R}_u(G)$ is the unipotent radical of $G$. ...
Added: February 28, 2023
Arzhantsev I., Zaitseva Y., Russian Mathematical Surveys 2022 Vol. 77 No. 4 P. 571–650
We survey recent results on open embeddings of the affine space C^n into a complete algebraic variety X such that the action of the vector group G_a^n on C^n by translations extends to an action of G_a^n on X. We begin with the Hassett–Tschinkel correspondence describing equivariant embeddings of \mathbb{C}^n into projective spaces and present its generalization for embeddings into projective hypersurfaces. Further sections deal with embeddings into flag ...
Added: February 26, 2023