## Papers of Takeshi HIRAI (Kyoto University)

1. Hirai, Takeshi, On irreducible representations of the Lorentz group of $n {\rm th}$ order. Proc. Japan Acad. 38 (1962), 258--262 [MR: 32#8844]
2. Hirai, Takeshi, On infinitesimal operators of irreducible representations of the Lorentz group of $n$ th order. Proc. Japan Acad. 38 (1962), 83--87 [MR: 25#2146]
3. Hirai, Takeshi, The characters of irreducible representations of the Lorentz group of $n$ th order. Proc. Japan Acad. 41 (1965), 526--531 [MR: 33#4185]
4. Hirai, Takeshi, Classification and the characters of irreducible representations of ${\rm SU}(p,\,1)$. Proc. Japan Acad. 42 (1966), 907--912 [MR: 36#6539]
5. Hirai, Takeshi, The Plancherel formula for the Lorentz group of $n {\rm th}$ order. Proc. Japan Acad. 42 (1966), 323--326 [MR: 34#5980]
6. Hirai, Takeshi, The characters of some induced representations of semi simple Lie groups. J. Math. Kyoto Univ. 8 (1968), 313--363 [MR: 39#354]
7. Hirai, Takeshi, The characters of some induced representations of semi simple Lie groups. Proc. Japan Acad. 44 (1968), 636--641 [MR: 38#3384]
8. Hirai, Takeshi, Invariant eigendistributions of Laplace operators on real simple Lie groups. I. Case of ${\rm SU}(p,q).$ Japan. J. Math. 39 (1970), 1--68. [MR: 53 13475]
9. Hirai, Takeshi, Characters of representations of real semisimple Lie groups and invariant eigendistributions. Sugaku 23 (1971), no. 4, 241--260. (in Japanese) [MR: 58 28287]
10. Hirai, Takeshi, Some remarks on invariant eigendistributions on semisimple Lie groups. J. Math. Kyoto Univ. 12 (1972), 393--411. [MR: 46 1967]
11. Hirai, Takeshi, The Plancherel formula for ${\rm SU}(p,\,q)$. J. Math. Soc. Japan 22 (1970), 134--179 [MR: 42#3230]
12. Hirai, Takeshi, Structure of induced representations and characters of irreducible representations of complex semisimple Lie groups. Lecture Notes in Math., Vol. 266 (1972), 167--188. [MR: 53 3204]
13. Hirai, Takeshi, Explicit form of the characters of discrete series representations of semisimple Lie groups. (1973). Amer. Math. Soc., Providence, R. I. [MR: 53 8329]
14. Hirai, Takeshi, Supplements and corrections to my paper J. Math. Kyoto Univ. 15 (1975), 237--250. [MR: 51 8339]
15. Hirai, Takeshi, A note on automorphisms of real semisimple Lie algebras. J. Math. Soc. Japan 28 (1976), no. 2, 250--256. [MR: 54 368]
16. Hirai, Takeshi, Invariant eigendistributions of Laplace operators on real simple Lie groups. II. General theory for semisimple Lie groups. Japan. J. Math. (N.S.) 2 (1976), no. 1, 27--89. [MR: 58 28273a]
17. Hirai, Takeshi, Invariant eigendistributions of Laplace operators on real simple Lie groups. III. Methods of construction for semisimple Lie groups. Japan. J. Math. (N.S.) 2 (1976), no. 2, 269--341. [MR: 58 28273b]
18. Hirai, Takeshi, Invariant eigendistributions of Laplace operators on real simple Lie groups. IV. Explicit forms of the characters of discrete series representations for ${\rm Sp}(n,\,{\bf R})$. Japan. J. Math. (N.S.) 3 (1977), no. 1, 1--48. [MR: 58 28273c]
19. Hirai, Takeshi, Character formulas for the discrete series for semisimple Lie groups. Lecture Notes in Math., 739 (1979), 315--340. [MR: 81i:22011]
20. Fronsdal, C., ; Hirai, T. [Hirai, Takeshi], A remark on the tensor product of irreducible representations of a compact Lie group. Japan. J. Math. (N.S.) 7 (1981), no. 1, 201--211. [MR: 85j:22025]
21. Hirai, Takeshi, The characters of the discrete series for semisimple Lie groups. J. Math. Kyoto Univ. 21 (1981), no. 3, 417--500. [MR: 83b:22018]
22. Hirai, Takeshi, On Richardson classes of unipotent elements in semisimple algebraic groups. Proc. Japan Acad. Ser. A Math. Sci. 57 (1981), no. 7, 367--372. [MR: 82k:17007]
23. Fronsdal, C.; Hirai, T. [Hirai, Takeshi], A note on a regularity of irreducible characters of a nonconnected Lie group. Proc. Japan Acad. Ser. A Math. Sci. 57 (1981), no. 1, 7--12. [MR: 82i:22014]
24. Hirai, Takeshi, Structure of unipotent orbits and Fourier transform of unipotent orbital integrals for semisimple Lie groups. in "Lectures on harmonic analysis on Lie groups and related topics (Strasbourg, 1979)", pp. 75--138, Lectures in Math., 14, Kinokuniya Book Store, Tokyo, 1982. [MR: 85a:22025]
25. Hirai, Takeshi, On the inducing of unipotent classes for semisimple algebraic groups. I. Case of exceptional type. Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 1, 37--40. [MR: 83f:20029a]
26. Hirai, Takeshi, On the inducing of unipotent classes for semisimple algebraic groups. II. Case of classical type. Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 2, 82--86. [MR: 83f:20029b]
27. Hirai, Takeshi, On semisimple Lie algebras over algebraically closed fields. Proc. Japan Acad. Ser. A Math. Sci. 60 (1984), no. 6, 225--228. [MR: 85h:17005]
28. Fronsdal, C., Hirai, Takeshi, Unitary representations of supergroups. in "Essays on supersymmetry", pp. 15--66, Math. Phys. Stud., 8, Reidel, Dordrecht, 1986. [CMP: 19 01]
29. Hirai, Takeshi, Unitary representations of a Lie superalgebra. in "Proceedings of the 14th ICGTMP (Seoul, 1985)", pp. 218--221, World Sci. Publishing, Singapore, 1986. [CMP: 18 16]
30. Furutsu, Hirotoshi, ; Hirai, Takeshi, On representations of Lie superalgebras. Proc. Japan Acad. Ser. A Math. Sci. 63 (1987), no. 7, 235--238. [MR: 88m:17020]
31. Furutsu, Hirotoshi, ; Hirai, Takeshi, Representations of Lie superalgebras. I. Extensions of representations of the even part. J. Math. Kyoto Univ. 28 (1988), no. 4, 695--749. [MR: 90f:17042]
32. Hirai, Takeshi, Some aspects in the theory of representations of discrete groups. Japan. J. Math. (N.S.) 16 (1990), no. 2, 197--268. [MR: 93e:22008]
33. Hirai, Takeshi, Some aspects in the theory of representations of discrete groups. I. Proc. Japan Acad. Ser. A Math. Sci. 66 (1990), no. 10, 315--318. [MR: 93g:22004]
34. Hirai, Takeshi, Some aspects in the theory of representations of discrete groups. II. Proc. Japan Acad. Ser. A Math. Sci. 66 (1990), no. 1, 16--18. [MR: 93g:22005]
35. Hirai, Takeshi, Construction of irreducible unitary representations of the infinite symmetric group ${\frak S}\sb \infty$. J. Math. Kyoto Univ. 31 (1991), no. 2, 495--541. [MR: 92i:20018]
36. Hirai, Takeshi, Irreducible unitary representations of the group of diffeomorphisms of a noncompact manifold. J. Math. Kyoto Univ. 33 (1993), no. 3, 827--864. [MR: 95h:22022]
37. Hirai, Takeshi, Representations of groups and quasi invariant measures. Surikaisekikenkyusho Kokyuroku (1994), No. 887 191--215. (in Japanese) [CMP: 96 07]
38. Hirai, Takeshi, Representations of diffeomorphism groups and the infinite symmetric group. in "Noncompact Lie groups and some of their applications (San Antonio, TX, 1993)", pp. 225--237, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 429, Kluwer Acad. Publ., Dordrecht, 1994. [MR: 96c:22036]
39. Hirai, Takeshi, and Shimomura, Hiroaki, Relations between unitary representations of diffeomorphism groups and those of the infinite symmetric group or of related permutation groups. Preprint, 1996.