arXiv subjects

Yoshiyuki Kimura

Publications and source records attributed to Yoshiyuki Kimura.

7 recordsLinked to original sources

arXiv2023

Twist automorphisms and Poisson structures

We introduce (quantum) twist automorphisms for upper cluster algebras and cluster Poisson algebras with coefficients. Our constructions generalize the twist automorphisms for quantum unipotent cells. We study their existence and their compatibility with Poisson structures and quantization. The twist automorphisms always permute well-behaved bases for cluster algebras. We explicitly construct (quantum) twist automorphisms of Donaldson-Thomas type and for principal coefficients.

math.QA↗

arXiv2019

Twist automorphisms on quantum unipotent cells and dual canonical bases

In this paper, we construct twist automorphisms on quantum unipotent cells, which are quantum analogues of the Berenstein-Fomin-Zelevinsky twist automorphisms on unipotent cells. We show that those quantum twist automorphisms preserve the dual canonical bases of quantum unipotent cells. Moreover, we prove that quantum twist automorphisms are described by the syzygy functors for representations of preprojective algebras in the symmetric case. This is the quantum analogue of Geiß-Leclerc-Schröer's description, and Geiß-Leclerc-Schröer's results are essential in our proof. As a consequence, we show that quantum twist automorphisms are compatible with quantum cluster monomials. The 6-periodicity of specific quantum twist automorphisms is also verified.

math.QA↗

arXiv2017

Quantum twist maps and dual canonical bases

In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincaré-Birkhoff-Witt type bases under the "reverse" lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors.

math.QA↗

arXiv2015

Remarks on quantum unipotent subgroup and dual canonical basis

We prove the tensor product decomposition of the half of quantized universal enveloping algebra associated with a Weyl group element which was conjectured by Berenstein and Greenstein.

math.QA↗

arXiv2012

Graded quiver varieties, quantum cluster algebras and dual canonical basis

Inspired by a previous work of Nakajima, we consider perverse sheaves over acyclic graded quiver varieties and study the Fourier-Sato-Deligne transform from a representation theoretic point of view. We obtain deformed monoidal categorifications of acyclic quantum cluster algebras with specific coefficients. In particular, the (quantum) positivity conjecture is verified whenever there is an acyclic seed in the (quantum) cluster algebra. In the second part of the paper, we introduce new quantizations and show that all quantum cluster monomials in our setting belong to the dual canonical basis of the corresponding quantum unipotent subgroup. This result generalizes previous work by Lampe and by Hernandez-Leclerc from the Kronecker and Dynkin quiver case to the acyclic case. The Fourier transform part of this paper provides crucial input for the second author's paper where he constructs bases of acyclic quantum cluster algebras with arbitrary coefficients and quantization.

math.RT↗

arXiv2010

Quantum Unipotent Subgroup and dual canonical basis

Geiss-Leclerc-Schroer defined the cluster algebra structure on the coordinate ring $C[N(w)]$ of the unipotent subgroup, associated with a Weyl group element $w$ and they proved cluster monomials are contained in Lusztig's dual semicanonical basis $S^{*}$. We give a set up for the quantization of their results and propose a conjecture which relates the quantum cluster algebras to the dual canonical basis ${B}^{up}$. In particular, we prove that the quantum analogue $O_{q}[N(w)]$ of ${C}[N(w)]$ has the induced basis from ${B}^{up}$, which contains quantum flag minors and satisfies a factorization property with respect to the `$q$-center' of $O_{q}[N(w)]$. This generalizes Caldero's results from ADE cases to an arbitary symmetrizable Kac-Moody Lie algebra.

math.QA↗

arXiv2007

Flight Performance of the AKARI Cryogenic System

We describe the flight performance of the cryogenic system of the infrared astronomical satellite AKARI, which was successfully launched on 2006 February 21 (UT). AKARI carries a 68.5 cm telescope together with two focal plane instruments, Infrared Cameras (IRC) and Far Infrared Surveyor (FIS), all of which are cooled down to cryogenic temperature to achieve superior sensitivity. The AKARI cryogenic system is a unique hybrid system, which consists of cryogen (liquid helium) and mechanical coolers (2-stage Stirling coolers). With the help of the mechanical coolers, 179 L (26.0 kg) of super-fluid liquid helium can keep the instruments cryogenically cooled for more than 500 days. The on-orbit performance of the AKARI cryogenics is consistent with the design and pre-flight test, and the boil-off gas flow rate is as small as 0.32 mg/s. We observed the increase of the major axis of the AKARI orbit, which can be explained by the thrust due to thermal pressure of vented helium gas.

astro-ph↗