Publications by Hans Plesner Jakobsen

1

(with M. Goto) On intersecting geodesics. Preprint Series 1972/73 No. 27, Aarhus Universitet

2

Conformal harmonic analysis and intertwining differential operators. In Group Theoretical Methods in Physics, pp. 573-576, Academic Press 1976

3

(with M. Vergne) Wave and Dirac operators, and representations of the conformal group , J. Functional Analysis 24, 52-106 (1977)

4

Intertwining differential operators for Mp(n,R) and SU(n,n), Trans. Amer. Math. Soc. 246, 311-337 (1978)

5

Tensor products, reproducing kernels, and power series, J. Functional Analysis , 293-305 (1979)

6

(with I. E. Segal, B. Speh, M. Vergne and B. Ørsted) Symmetry and causality properties of physical fields, Proc. Natl. Acad. Sci. U. S. A. , 1609-1611 (1978)

7

(with M. Vergne) Restrictions and expansions of holomorphic representations, J. Functional analysis , 29-53 (1979)

8

Higher order tensor products of wave equations. In Non-Commutative Harmonic Analysis, Proceedings, Marseille-Luminy France; Lecture notes in mathematics 728, 97-115, Springer Verlag (1979)

9

(with M. Kon and I. E. Segal) Angular Momentum of the cosmic background radiation, Phys. Rev. Letters 42, 1788-1791 (1979)

10

On singular holomorphic representations, Invent. Math. 62, 67-78 (1980)

11

(with S. Paneitz, I. E. Segal, B. Speh and B. Ørsted) Covariant chronogeometry and extreme distances. II: Elementary particles, Proc. Natl. Acad. Sci. U. S. A. 78, 5261-5265(1981)

12

(with M. Harris) Singular holomorphic representations and singular modular forms, Math. Ann. 259, 227-244 (1983)

13

The last possible place of unitarity for certain highest weight modules, Math. Ann. 256, 439-447 (1981)

14

Group theoretical aspects of the chronometric theory. In Differential Geometric Methods in Mathematical Physics, Proceedings, Clausthal 1980; Lecture Notes In Mathematics bf 905, 165-169, Springer Verlag (1982)

15

Hermitian symmetric spaces and their unitary highest weight modules , J. Functional Analysis 52, 385-412 (1983)

16

(with M. Harris) Covariant differential operators. In Group Theoretical Methods In Theoretical Physics, Proceedings, Istanbul 1982, 16-34. Lecture Notes in Physics 180, Springer Verlag (1983)

17

Basic covariant differential operators on hermitian symmetric spaces, Ann. scient. Èc. Norm. Sup. 18, 421-436 (1985)

18

Subspace structures of holomorphic representations. In Sixteen research reports by the Niels Bohr fellows of the royal Danish Academy of science and letters, 22-33 (1985)

19

(with V. Kac) A new class of unitarizable highest weight representations of infinite dimensional Lie algebras, In: ``Springer Lecture Notes in Physics 226, 1-20 (1985)

20

Conformal covariants, Publ. RIMS Kyoto University 22, 345-364 (1986)

21

A spin-off from highest weight representations; conformal covariants, in particular for O(3, 2), In: ``Symposium on conformal groups and structures, Proceedings, Clausthal 1985'', Lecture Notes in Physics 261, 253-265 (1986)

22

On the range of unitarity for highest weight representations of classical Lie superalgebras, In: ``Symposium on Topological and Geometrical Methods in Field Theory, Espoo, 1986'', 103-109, World Scientific, Singapore

23

Højeste-Vægt Moduler. Tensorprodukter, Unitaritet, Differentialoperatorer. ``Doktorafhandling'' (Danish Doctoral Dissertation), March 1988

24

(with V. Kac) A new class of unitarizable highest weight representations of infinite dimensional Lie algebras#2, jour J. Functional analysis , 69-90 (1989)

25

(with B. Durhuus and R. Nest) Topological quantum field theories from 6j-symbols, Rev. Math. Phys. l5, 1-67 (1993)

26

(with B. Durhuus and R. Nest) A construction of topological quantum field theories from 6j--symbols, Nucl. Physics B (Proc. Suppl.) , 109--121 (1992)

27

(with B. Durhuus and R. Nest) Topological field theories from quantum 6j-symbols. In: ``Topological and Geometrical Methods in Field Theory, Turku (1992)'', 121--134, World Scientific, Singapore

28

A classification of the unitarizable highest weight modules for affine Lie superalgebras, J. Functional Analysis , 422--457 (1994)

29

The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras , Memoirs of the A.M.S. , Nr. 532, 116pp (1994)

30

An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties, Compositio Math. 101, 313--352 (1996)

31

Tensoring with small quantized representations. J. Math. Phys. 38, 4323--4335 (1997)

32

Quantized hermitian symmetric spaces. In: ``Lie Theory and its Applications in Physics'', 105-116, World Scientific, Singapore (1996)

33

(with H. Zhang) The center of the Quantized Matrix Algebra. J. Algebra 196, 458--474 (1997)

34

(with H. Zhang) The center of the Dipper Donkin quantized matrix algebra. Beiträge Algebra Geom. 38, 411--421 (1997)

35

(with A. Jensen, S. Jøndrup, and H. Zhang) Quadratic algebras of type AIII. I II III. Tsinghua Science and Technology 3, 1199--1202, 1203--1208, 1209--1212 (1998)

36

Unitarity of highest weight modules for quantum groups. Lett. Math. Phys. 42, 119--133 (1997)

37

(with H. Zhang) Cyclic representations of the quantum matrix algebras. Comm. Algebra 27, 493--510 (1999)

38

(with H. Zhang) A class of quadratic matrix algebras arising from the quantized enveloping algebra. J. Math. Phys. 41, 2310--2336 (2000)

39

(with H. Zhang) Quantized Heisenberg Space. Algebras and Representation Theory 3, 151--174 (2000).

40

(with S. Jøndrup) Quantized Rank R Matrices. J. Algebra 246, 70--96 (2001)

41

Q-differential operators. Preprint (19pp) 1999 ( http://xxx.lanl.gov/abs/math.QA/9907009)

42

Quantized Dirac operators. Czech. J. Phys. 50, 1265--1270 (2000)

43

(with C.-W. H. Lee) Unitary Irreducible Representations of a Lie Algebra for Open Matrix Chains. In " Theoretical high energy physics; MRST 2000". AIP Conference Proceedings 541, 130-139 (2000) New York

44

(with C.-W. H. Lee) Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models. J. Math. Phys. 42, 3817--3838 (2001)

45

Quantized symmetrizations and *-products. In "Quantum Groups and Symmetries", Proceedings, Krakow, 2001, 396-403. World Scientific, Singapore.

46

(with C.-W. H. Lee) Matrix Chain Models and Kac-Moody Algebras "Vertex Operators and Kac-Moody algebras". Proceedings, Madras 2002, Contemp. Math. 343, 147-165, A.M.S.

47

Matrix Chain Models and their $q$-deformations (14pp) To appear in the Proceedings of 5th International Workshop ``Lie Theory and Its Applications in Physics'', 16 - 22 June 2003, Varna, Bulgaria.

48

(with H. Zhang) The Exponential Nature and Positivity Algebr. Represent. Theor. 9, 267-284 (2006)

49

(with H. Zhang) The quantum cluster algebra structure on quantum matrices. 1st draft Feb. 08

50

(with C. Pagani) The Structure of the Dipper Donkin Algebra as a Cluster Algebra. 1st draft Feb. 08

51

Inducing from indecomposable modules of a maximal parabolic: Covariant Differential Operators. 0th draft.