Kyo Nishiyama and Chen-bo Zhu,
Theta lifting of unitary lowest weight modules and their associated cycles.
Duke Math. J., 125(2004), 415 -- 465.
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Kyo Nishiyama, Hiroyuki Ochiai and Chen-bo Zhu,
Theta lifting of nilpotent orbits for symmetric pairs.
Trans. Amer. Math. Soc. 358 (2006), no. 6, 2713--2734.
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Kyo Nishiyama,
A note on affine quotients and equivariant double fibrations.
Infinite dimensional harmonic analysis III, 197--212, World Sci. Publ.,
Hackensack, NJ, 2005.
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Kyo Nishiyama, Classification of spherical nilpotent orbits for U(p, p). J. Math. Kyoto Univ., 44 (2004), 203 -- 215.
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Makoto Matsumoto, Kyo Nishiyama and Masamichi Yano, A Generator of H^1(M^1_g; H^1(\Sigma_g; Z)) and a Reflection Representation of the Mapping Class Groups via Iwahori-Hecke Algebras. Progress of Theoretical Physics Supplement No.144 (2002), 141--144.
Kyo Nishiyama and Chen-bo Zhu, Theta lifting of holomorphic discrete series: the case of ${\rm U}(n,n)\times{\rm U}(p,q)$. Trans. Amer. Math. Soc. 353 (2001), no. 8, 3327--3345.
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Kyo Nishiyama, Hiroyuki Ochiai, and Kenji Taniguchi, Bernstein degree and associated cycles of Harish-Chandra modules---Hermitian symmetric case. Nilpotent orbits, associated cycles and Whittaker models for highest weight representations. Ast\'erisque No. 273 (2001), 13--80.
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Kyo Nishiyama, Multiplicity-free actions and the geometry of nilpotent orbits. Math. Ann., 318 (2000), 777 -- 793.
Akihiko Gyoja, Kyo Nishiyama and Kenji Taniguchi, Invariants for Representations of Weyl Groups, Two-sided Cells, and Modular Representations of Iwahori-Hecke Algebras. Adv. Studies in Pure Math., 28 (2000), 103 -- 112.
Akihiko Gyoja, Kyo Nishiyama and Kenji Taniguchi, Kawanaka invariants for representations of Weyl groups. J. Alg., 225 (2000), 842 - 871.
Kyo Nishiyama, Theta lifting of two-step nilpotent orbits for the pair $ O(p, q) \times Sp(2n, \R) $. In H. Heyer, T. Hirai and N. Obata (eds.), ``Infinite Dimensional Harmonic Analysis'', Transactions of a Japanese-German Symposium held from September 20th to 24th, 1999 at Kyoto University, pp. 278 -- 289, Kyoto 1999.
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Kyo Nishiyama and Hiroyuki Ochiai, Bernstein degree of singular unitary highest weight representations of the metaplectic group. Proc. Japan Acad., Ser. A, 75 (1999), 9 - 11.
A. Gyoja, Kyo Nishiyama and H. Shimura. Invariants for representaions of Weyl groups and two-sided cells. J. Math. Soc. Japan, 51 (1999), 1 - 34.
Kyo Nishiyama, Schur duality for Cartan type Lie algebra $ W_n $. Journal of Lie Theory, 9 (1999), 234 - 248.
Zixin Hou, Shaoqiang Deng, Soji Kaneyuki and Kyo Nishiyama, Dipolarizations in semisimple Lie algebras and homogeneous parak\"{a}hler manifolds. Journal of Lie Theory, 9 (1999), 215 - 232.
Kyo Nishiyama, Commutant algebra and harmonic polynomials of a Lie algebra of vector fields. J. Alg., 183(1996), 545 -- 559.
misprint がありました。詳しくは こちらを御覧下さい。
Kyo Nishiyama and Haiquan Wang, Commutant algebra of Cartan-type Lie superalgebra $ W(n) $. J. Math. Kyoto Univ., 36(1996), 129 -- 142.
平井先生の還暦献呈論文です。しかしタイトルの下に献呈の辞を入れるのを忘れ、Introduction の方に入っています。
Kyo Nishiyama and Haiquan Wang, Commutant algebra of superderivations on a Grassmann algebra. Proc. Japan Acad., 72 Ser. A (1996), 8 -- 11.
Kyo Nishiyama, Super dual pairs and highest weight modules of orthosymplectic algebras. Adv. in Math., 104(1994), 66--89.
Hirotoshi Furutsu and Kyo Nishiyama, Realization of irreducible unitary representations of $ {\frak osp}(M/N; {\Bbb R}) $ on Fock spaces. in Proceedings of Fuji-Kawaguchiko Conference on Representation Theory of Lie Groups and Lie Algebras, edited by T. ~Kawazoe et. al., pp1--21, World Scientific, 1992.
Kyo Nishiyama, Distribution characters of a semisimple Lie group and representations of Weyl groups and their Hecke algebras. Sugaku Expositions, 5(1992), 15-33.
Hirotoshi Furutsu and Kyo Nishiyama, Classification of irreducible super unitary representations of $ {\frak su}(p,q/n) $. Comm. in Math. Phys., 141(1991), 475--502.
Kyo Nishiyama, Decomposing oscillator representations of $ {\frak osp}(2n/n; {\Bbb R}) $ by a super dual pair $ {\frak osp}(2/1; { \Bbb R}) \times {\frak so}(n) $. Comp. Math., 80(1991), 137--149.
Kyo Nishiyama, Characters and super-characters of discrete series representations for orthosymplectic Lie superalgebras. J. Alg., 141(1991), 399--419.
Kyo Nishiyama, Oscillator representations for orthosymplectic algebras. J. Alg., 129(1990), 231--262.
Kyo Nishiyama, Algebraic structures on virtual characters of a semisimple Lie group. Adv. Stud. in Pure Math., 14(1988), 417--468.
Kyo Nishiyama, Generators and relations for a certain Hecke algebra. Research Activities, Faculty Sci. Engineering, Tokyo Denki Univ., 8--9(1987), 9--14.
Kyo Nishiyama, Representations of Weyl groups and their Hecke algebras on virtual character modules of a semisimple Lie group (Th\ `ese). J. Math. Kyoto Univ., 27(1987), 151--181.
博士論文です。 MathReview には「なぜこのような作用を考えるのかはっきりしない」とまで書かれて酷評されていますが、特異な無限小指標の場合にちゃんと指標の次元(つまり既約表現の個数ですね)が Hecke 環の表現の言葉で書けるだけでもいいと自分では思っています。もちろん他にも応用はあるはずなのですが、自分自身取り組んでいないのは反省点。
Kyo Nishiyama, Open problems on character polynomials and Gelfand-Kirillov dimensions of virtual characters. In Open problems in representation theory of Lie groups, Proceedings of the conference on ``Analysis on homogeneous spaces" held at Katata, 1986.
これは論文ではないですね(しかし文部省むけの業績表にはちゃっかり入れてます)。別刷(他の人の Open Problems も含む)はたくさん余っています。請求して下さい。図書館には入っていないと思うんですが。
Kyo Nishiyama, Virtual characters and constant coefficient invariant eigendistributions on a semisimple Lie group. Japan. J. Math., New Series, 12(1986), 75--94.
Kyo Nishiyama, Representations of Hecke algebras on virtual character modules of a semisimple Lie group. Proc. Japan Acad., 62(1986), 159--162.
Kyo Nishiyama, Virtual characters and constant coefficient invariant eigendistributions on a semisimple Lie group. Proc Japan Acad., 61(1985), 168--171.
Kyo Nishiyama, Virtual character modules of semisimple Lie groups and representations of Weyl groups. J. Math. Soc. Japan, 37(1985), 719--740.
Kyo Nishiyama, Representations of Weyl group and its subgroups on the virtual character modules. Proc. Japan Acad., 60(1984), 193--196.
Kyo Nishiyama, Decompositions of tensor products of infinite and finite dimensional representations of semisimple groups. J. Math. Kyoto Univ., 25(1985), 1--20.
西山享, 零錐の特異点解消と余法束
2006年度 表現論シンポジウム講演集 原稿 (19 pages)
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西山享, Spherical Nilpotent Orbits for Symmetric Pairs -- The case of $U(p, p)$ --
数理解析研究所講究録 1245 「新世紀への表現論と調和解析」 (2002.1), 135 -- 146.
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表現論の方法と考え方 [名古屋大学 ('00/11) での集中講義ノート]
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西山享,
巾零軌道とリー群の表現論
[代数学シンポジウム
(九州大学六本松キャンパス)
August 9, 2000 における講演
``Theta lifting of representations and geometry of nilpotent orbits''
の報告]
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Kyo Nishiyama and Chen-Bo Zhu,
Theta lifting of the trivial representation
and the associated nilpotent orbit
--- the case of $ U(p, q) \times U(n, n) $ ---.
[A note for ``Proceedings of Symposium on Representation Theory 1999'' in Tateyama, Chiba]
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極小表現入門 [東大 ('98/12) での集中講義ノート]
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対称式と調和多項式に関する講義ノート[和歌山大学集中講義用]('98/1/5)
目次/群とあそぼう(復習)/対称群の作用する空間/線型群のお話/対称式と調和多項式/多項式環上の対称群の表現 [計 50 ページ]
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Restriction of the irreducible representations of $ GL_n $ to the symmetric group $ \lie{S}_n $.
It is well-known that the 0-weight space of the irreducible representation of $ GL_n $ with highest weight of size $ n $ is irreducible for $ {\frak S}_n $. This note is a generalization of such kind of phenominon. A relation to the plethysm is also dicussed.
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'96 整数論サマースクール報告集用の原稿です。演習問題までつけました (^^;;
学生の方を鍛えるのに使ってもらえば嬉しいです。
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西山享著 「よくわかる幾何学 -複素平面・初等幾何学・射影幾何学をめぐって-」 丸善 2004年2月29日発行 [ISBN 4-621-07370-2]
西山享著 「基礎課程 微分積分 I -- 1 変数の微積分 --」 サイエンス社、1998年12月10日初版発行 [ISBN4-7819-0894-2]
西山享著 「基礎課程 微分積分 II -- 多変数の微積分と微分方程式 --」 サイエンス社、1998年12月10日初版発行 [ISBN4-7819-0895-0]
西山享著「多項式のラプソディー」はじめよう数学2 日本評論社、1999年3月25日初版発行 [ISBN4-535-60841-5]
落合さん@九州大学による ミスプリ、間違い情報
K. M. ヒール、M.L.ハンセン、K.M.リカード著/示野信一他訳「Maple V リリース5 ラーニングガイド」 シュプリンガー・フェアラーク東京、1998年9月25日発行 [ISBN4-431-70776-X] (共訳)
D.コックス/J.リトル/D.オシー 著 落合啓之/示野信一/西山享/室政和/山本敦子 訳 「グレブナ基底と代数多様体入門(上) イデアル・多様体・アルゴリズム」 A5 407頁 価格(本体3,800+税) [ISBN 4-431-70823-5] (共訳)
D.コックス/J.リトル/D.オシー 著 落合啓之/示野信一/西山享/室政和/山本敦子 訳 「グレブナ基底と代数多様体入門(下) イデアル・多様体・アルゴリズム」 A5 417頁 価格(本体3,800+税) [ISBN 4-431-70824-3] (共訳)
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