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European Mathematical Society Publishing House
2024-03-29 11:52:27
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Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
51
2015
1
On WKB Theoretic Transformations for Painlevé Transcendents on Degenerate Stokes Segments
Kohei
Iwaki
Kyoto University, KYOTO, JAPAN
exact WKB analysis, Painlevé equations
The WKB theoretic transformation theorem established in [KT2] implies that the first Painlevé equation gives a normal form of Painlevé equations with a large parameter near a simple $P$-turning point. In this paper we extend this result and show that the second Painlevé equation $(P_{II})$ and the third Painlevé equation $(P_{III'(D_7)})$ of type $D_7$ give a normal form of Painlevé equations on a degenerate $P$-Stokes segments connecting two different simple $P$-turning points and on a degenerate $P$-Stokes segment of loop-type, respectively. That is, any 2-parameter formal solution of a Painlevé equation is reduced to a 2-parameter formal solution of $(P_{II})$ or $(P_{III'(D_7)})$ on these degenerate $P$-Stokes segments by our transformation.
Ordinary differential equations
1
57
10.4171/PRIMS/148
http://www.ems-ph.org/doi/10.4171/PRIMS/148
Classification of Finite-Dimensional Irreducible Representations of Generalized Quantum Groups via Weyl Groupoids
Saeid
Azam
University of Isfahan, ISFAHAN, IRAN
Hiroyuki
Yamane
University of Toyama, TOYAMA, JAPAN
Malihe
Yousofzadeh
University of Isfahan, ISFAHAN, IRAN
Lie superalgebras, Nichols algebras, quantum groups
Let $\chi$ be a bi-homomorphism over an algebraically closed fi eld of characteristic zero. Let $U(\chi) $) be a generalized quantum group, associated with $\chi$ , such that dim$U^+(\chi ) = \infty$, $\| \mathbb R^+(\chi)| < \infty$, and $R^+(\chi)$ is irreducible, where $U^+(\chi)$ is the positive part of $U(\chi)$, and $R^+(\chi)$ is the Kharchenko positive root system of $U^+(\chi)$. In this paper, we give a list of fi nite-dimensional irreducible $U(\chi)$-modules, relying on a special reduced expression of the longest element of the Weyl groupoid of $R(\chi) := R^+(\chi) \cup (–R^+(\chi))$. From the list, we explicitly obtain lists of finite-dimensional irreducible modules for simple Lie superalgebras $\mathfrak g$ of types A–G and the (standard) quantum superalgebras $U_q(\mathfrak g)$. An intrinsic gap appears between the lists for $\mathfrak g$ and $U_q(\mathfrak g)$, e.g, if $≥\mathfrak g$ is B$(m, n)$ or D$(m, n)$.
Nonassociative rings and algebras
59
130
10.4171/PRIMS/149
http://www.ems-ph.org/doi/10.4171/PRIMS/149
From the Drinfeld Realization to the Drinfeld–Jimbo Presentation of Affine Quantum Algebras: Injectivity
Ilaria
Damiani
Università di Roma 'Tor Vergata', ROMA, ITALY
quantum groups
The surjective homomorphism $\psi$ (see [Da1]) from the Drinfeld realization $U^{Dr}_q$ to the Drinfeld and Jimbo presentation $\mathcal U^{DJ}_q$ of affi ne quantum algebras is proved to be injective. A consequence of the arguments used in the paper is the triangular decomposition of the Drinfeld realization of a ne quantum algebras also in the twisted case. A presentation of affi ne Kac–Moody algebras in terms of "Drinfeld generators" is also provided.
Nonassociative rings and algebras
131
171
10.4171/PRIMS/150
http://www.ems-ph.org/doi/10.4171/PRIMS/150
The Bishop–Phelps–Bollobás Property: a Finite-Dimensional Approach
María
Acosta
Universidad de Granada, GRANADA, SPAIN
Julio
Becerra Guerrero
Universidad de Granada, GRANADA, SPAIN
Domingo
García
Universitat de Valencia, BURJASSOT (VALENCIA), SPAIN
Sun Kwang
Kim
Kyonggi University, SUWON, SOUTH KOREA
Manuel
Maestre
Universitat de Valencia, BURJASSOT (VALENCIA), SPAIN
Bishop–Phelps–Bollobás theorem, Banach space, $c_0$
Our goal is to study the Bishop–Phelps–Bollobás property for operators from $c_0$ into a Banach space. We fi rst characterize those Banach spaces $Y$ for which the Bishop–Phelps–Bollob ás property holds for ($\ell^3_{\infty}, Y)$. Examples of spaces satisfying this condition are provided.
Functional analysis
Operator theory
173
190
10.4171/PRIMS/151
http://www.ems-ph.org/doi/10.4171/PRIMS/151
The Spaces of Analytic Functions on Open Subsets of $\mathbb R^{\mathbb N}$ and $\mathbb C^{\mathbb N}$
José
Ansemil
Universidad Complutense de Madrid, MADRID, SPAIN
Jerónimo
López-Salazar
Universidad Politécnica de Madrid, MADRID, SPAIN
Socorro
Ponte
Universidad Complutense de Madrid, MADRID, SPAIN
analytic function, locally convex topology, inductive limit
This paper is devoted to study the space $\mathcal{A}\left( U\right)$ of all analytic functions on an open subset $U$ of $\mathbb{R}^{\mathbb{N}}$ or $\mathbb{C}^{\mathbb{N}}$. It is proved that if $U$ satisfies a weak condition (that will be called 0-property), then every $f\in \mathcal{A}\left( U\right) $ depends only on a finite number of variables. Then several topologies on $\mathcal{A}\left( U\right) $ are studied: the compact open topology, the $\tau_{\delta}$ topology (already known in spaces of holomorphic functions) and a new one, defined by the inductive limit of the subspaces of analytic functions which only depend on the first variables.
Functional analysis
191
206
10.4171/PRIMS/152
http://www.ems-ph.org/doi/10.4171/PRIMS/152