Yutaka YOSHIIAssociate Professor
■Researcher basic information
Organization
- College of Education Training Course for School Teachers Program for Subject Education ／ Major in Mathematics Education
- Graduate School of Education（Course for Professional degree ） Division of Professional Teacher Education Professional Course in School Subjects
- Faculty of Basic Natural Science Domain of Mathematics and Informatic
Research Keyword
Educational Background
Career
■Research activity information
Paper
- Generating sets of the Jacobson radical of the hyperalgebra of (SL2)r
Yutaka Yoshii
Journal of Computational Algebra, Feb. 2024, [Reviewed] - Certain linear isomorphisms for hyperalgebras relative to a Chevalley group
Yutaka Yoshii
Journal of Algebra and Its Applications, Jan. 2024, [Reviewed] - Some results on certain finite-dimensional subalgebras of the hyperalgebra of a universal Chevalley group
Yutaka Yoshii
Journal of Lie Theory, Dec. 2022, [Reviewed] - A basis of a certain module for the hyperalgebra of (SL2)r and some applications
Yutaka Yoshii, In the hyperalgebra Ur of the rth Frobenius kernel (SL2)r of the algebraic group SL2, we construct a basis of the Ur-module generated by a certain element which was given by the author before. As its applications, we also prove some results on the Ur-modules and the algebra Ur., World Scientific
Journal of Algebra and Its Applications, Sep. 2022, [Reviewed] - Utilization of mathematical knowledge in history education: from land surveying practice
M.Chiba; Y.Yoshii; T.Onishi
茨城大学教育実践研究, Dec. 2019 - Projective modules for the subalgebra of degree 0 in a finite-dimensional hyperalgebra of type A_1
Yutaka Yoshii
Proceedings of the American Mathematical Society, May 2018, [Reviewed] - 小学校算数科における学習内容の統合的・発展的な扱い
小口祐一; 梅津健一郎; 栗原博之; 松村初; 吉井豊
茨城大学教育学部紀要（教育科学）, 2018 - A tensor product of the Steinberg module and a certain simple kG(p(r))-module
Yutaka Yoshii, Let G be a connected, semisimple, and simply connected algebraic group defined and split over the finite field of order p, and let G(q) be the corresponding finite Chevalley or twisted group, where q=p(r). Recently, Anwar determines the direct sum decomposition of the tensor product of the rth Steinberg module and a simple G-module with a (p,r)-minuscule highest weight . In this paper, we determine that of the tensor product regarded as a module for G(q) under some weak assumptions for ., TAYLOR & FRANCIS INC
COMMUNICATIONS IN ALGEBRA, 2017, [Reviewed] - Primitive Idempotents of the Hyperalgebra for the r-th Frobenius kernel of SL(2, k)
Yutaka Yoshii, In this paper we construct primitive idempotents of the hyperalgebra for the r-th Frobenius kernel of the algebraic group SL(2, k)., HELDERMANN VERLAG
JOURNAL OF LIE THEORY, 2017, [Reviewed] - A generalization of Pillen's theorem for principal series modules II
Yutaka Yoshii, Let G be a connected, semisimple and simply connected algebraic group and G(q) the corresponding finite Chevalley group over the finite field of order q = p(r). In a recent paper the author determined a direct sum decomposition of the kG(q)-submodule generated by a highest weight vector of a certain Weyl module when q is not too small, which is a generalization of Pillen's result in 1997. In this article, we claim that the result does not need the assumption on q. (C) 2015 Elsevier Inc. All rights reserved., ACADEMIC PRESS INC ELSEVIER SCIENCE
JOURNAL OF ALGEBRA, May 2015, [Reviewed] - A Remark on Pillen's Theorem for Projective Indecomposable kG(n)-Modules
Yutaka Yoshii, Let g be a connected, semisimple and simply connected algebraic group defined and split over the finite field of order p, and let g(n) be the corresponding finite Chevalley group and g(n) the n-th Frobenius kernel. Pillen has proved that for a 3(h - 1)-deep and p(n)-restricted weight lambda, the G-module Q(n)(lambda) which is extended from the G(n)-PIM for lambda has the same socle series as the corresponding kG(n)-PIM U-n(lambda). Here we remark that this fact already holds for lambda being 2(h - 1)-deep., HELDERMANN VERLAG
JOURNAL OF LIE THEORY, 2013, [Reviewed] - A GENERALIZATION OF PILLEN'S THEOREM FOR PRINCIPAL SERIES MODULES
Yutaka Yoshii, Let G be a connected, semisimple and simply connected algebraic group defined and split over the finite field of order p. Pi lien proved in 1997 that the highest weight vectors of some Weyl C-modules generate the principal series modules as submodules for the corresponding finite Chevalley groups. This result is generalized in this paper., AMER MATHEMATICAL SOC
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, Nov. 2012, [Reviewed] - ON THE FROBENIUS-PERRON EIGENVALUES OF CARTAN MATRICES FOR SOME FINITE GROUPS
Yutaka Yoshii, We study integrality of the Frobenius-Perron eigenvalues of the Cartan matrices for the principal blocks of some finite groups of Lie type with noncyclic abelian Sylow p-subgroups., WORLD SCIENTIFIC PUBL CO PTE LTD
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, Jun. 2011, [Reviewed] - Eigenvalues of Cartan matrices of principal 3-blocks of finite groups with abelian Sylow 3-subgroups
Shigeo Koshitani; Yutaka Yoshii, Let A be the principal 3-block of a finite group G with an abelian Sylow 3-subgroup P. Let C(A) be the Cartan matrix of A. and we denote by rho(C(A)) the unique largest eigenvalue of C(A). The value rho(C(A)) is called the Frobenius-Perron eigenvalue of C(A). We shall prove that rho(C(A)) is a rational number if and only if A and the principal 3-block of N(G)(P) are Morita equivalent. This generalizes earlier Wada's theorem in 2007, where he proves it only for the case that the order of P is nine, while we prove it for the case that P is an arbitrary finite abelian 3-group. The result presented here uses the classification of finite simple groups. (C) 2010 Elsevier Inc. All rights reserved., ACADEMIC PRESS INC ELSEVIER SCIENCE
JOURNAL OF ALGEBRA, Oct. 2010, [Reviewed] - Broue's conjecture for the nonprincipal block of SL(2, q) with full defect
Yutaka Yoshii, M. Broue gives an important conjecture which is called Broue's abelian defect group conjecture. This conjecture says that a p-block, where p is a prime number, of a finite group with an abelian defect group is derived equivalent to its Brauer correspondent in the normalizer of the defect group. In this paper, we prove that this conjecture is true for the nonprincipal block of SL(2, p(n)) for a positive integer n. (C) 2009 Elsevier Inc. All rights reserved., ACADEMIC PRESS INC ELSEVIER SCIENCE
JOURNAL OF ALGEBRA, May 2009, [Reviewed]
Lectures, oral presentations, etc.
- Some elements of the hyperalgebra of SL(2,k) in positive characteristic and their applications
吉井 豊
RIMS共同研究（公開型）「組合せ論的表現論の発展」, 16 Oct. 2024, [Invited] - Some commutation formulas and linear isomorphisms for the hyperalgebra of a simple algebraic group
吉井 豊
第56回環論および表現論シンポジウム, 16 Sep. 2024 - 単純代数群の超代数における積が定めるいくつかの線形同型写像
吉井 豊
日本数学会秋季総合分科会, 04 Sep. 2024 - 単純代数群の超代数のある部分代数に関するいくつかの結果
吉井 豊
日本数学会年会, 15 Mar. 2023, 日本数学会
20230315, 20230318 - Structure of certain modules for the hyperalgebra Dist((SL_2)_r)
Yutaka Yoshii
日本数学会年会, Mar. 2022 - 超代数Dist(SL_{2,r})のJacobson根基の生成系
吉井 豊
日本数学会年会, Mar. 2019 - 代数群SL(2,k)のFrobenius核の超代数における次数0の部分代数の表現
第23回代数学若手研究会, Mar. 2018 - A tensor product of certain two simple modules for finite Chevalley groups
RIMS研究集会「有限群・代数的組合せ論・頂点作用素代数の研究」, Dec. 2016 - A direct sum decomposition of the kG(p^r)-submodule generated by the highest weight vector of a certain Weyl G-module
Yutaka Yoshii
RIMS研究集会「有限群のコホモロジー論とその周辺」, Feb. 2015 - 有限Chevalley群の2(h-1)-deepなウェイトに対する射影直既約加群のLoewy列
吉井 豊
日本数学会年会, Mar. 2013 - Generators in the socle series for principal series modules
Yutaka Yoshii
研究集会「有限群の表現論およびその周辺」, Sep. 2012 - Weyl加群の最高ウェイトベクトルが生成するkG(n)-加群
吉井 豊
日本数学会年会, Mar. 2012 - Weyl modules and principal series modules
Yutaka Yoshii
RIMS研究集会「組合せ論的表現論の拡がり」, Oct. 2011 - 有限群のブロックに対するCartan行列の固有値
越谷 重夫; 吉井 豊
日本数学会秋季総合分科会, Sep. 2010 - 2次の有限特殊線形群の非主ブロックのBroue予想
吉井 豊
日本数学会年会, Mar. 2010 - いくつかのLie型有限群のブロックに対するCartan行列の最大固有値
吉井 豊
日本数学会年会, Mar. 2010 - Eigenvalues of Cartan matrices for group algebras of finite groups
Yutaka Yoshii
RIMS研究集会「代数的組合せ論および関連する群と代数」, Nov. 2009 - Broue's conjecture of SL(2,q) in the defining characteristic
Yutaka Yoshii
第11回代数群と量子群の表現論研究集会, May 2008 - Nonprincipal block of SL(2,q)
Yutaka Yoshii
RIMS研究集会「有限群のコホモロジー論の研究」, Aug. 2007
Research Themes
