### Members of the Lie unit

## Professor Hrvoje Kraljević

**Position:**

- Retired full professor at the Department of Mathematics, Faculty of Science, University od Zagreb

**Education:**

- PhD in Mathemacs on February 28, 1973, Faculty of Science, University of Zagreb, with dissertation „Representations of the Group SU(n,1) and of Its Universal Covering Group“, mentor Svetozar Kurepa
- MSc in Mathematics on November 6, 1968, Faculty of Science, University of Zagreb, with thesis „Induced Representations of Locally Compact Groups and Some Applications“, mentor Svetozar Kurepa
- Bachelor’s degree in Theoretical Physics on November 16, 1966, Faculty of Science, University of Zagreb, with thesis „Group Representations and Applications in the Theora of Symmetries of Elemetary Particles“, mentor Svetozar Kurepa
- completed secondary schooling 1962 at the Classical Gymnasium in Zagreb

**Academic career:**

- 1966–1973 Assistant, Department of Mathematics, Faculty of Science, University of Zagreb
- 1973–1976 Assistant Professor (Dozent), Department of Mathematics, Faculty of Science, University of Zagreb
- 1976–1981 Associate Professor, Department of Mathematics, Faculty of Science, University of Zagreb
- from 1981 Full Professor, Department of Mathematics, Faculty of Science, University of Zagreb
- from 1990 Full Professor with tenure, Department of Mathematics, Faculty of Science, University of Zagreb

**Specializations:**

- February 1997, Institut für Mathematik der Universität „Karl Franzens“ Graz, Austria
- March 1981, Libera Università degli Studi, Trento, Italy
- March 1979, Libera Università degli Studi, Trento, Italy
- March–April 1978, École Polytechnique, Palaiseau, France
- 1974/75 Institute for Advanced Study, Princeton, USA

**Fields of interest:**

- Representation theory of Lie grouops and algebras
- Banach algebras, C*–algebras
- Operator theory on Hilbert spaces

**Five selected publications:**

- Kraljević, Representations of the universal covering group of the group SU(n,1), Glasnik Mat. 8(28) (1973), 23-72.
- Kraljević, On representations of the group SU(n,1), Trans. Amer. Math. Soc. 221(1976) (1976), 433-448.
- Kraljević, A note on nonunitary principal series representations, Proc. Amer. Math. Soc. 70 (1978), 213-216.
- Baldoni Silva, H.Kraljević, Composition factors for the principal series representations of the groups Sp(n,1), Trans. Amer. Math. Soc. 262 (1980), 447-471.
- Kraljević,S.Suljagić, K.Veselić, Index in semisimple Banach algebras, Glasnik Mat. 17(37) (1982), 73-95.

**Scientific grants (as principal investigator):**

- 2008–2014 a project of the Croatian Ministry of science, education and sports, code 037–0372794–3229, title „Representations of semisimple Lie groups; K–types, duals, C*–algebras“
- 1997–2001 a project of the Croatian Ministry of science and technology, code 037003, title „Functionalnoanalytic, geometric and algebraic aspects of representation theory of real Lie groups“
- 1993–1996 a project of the Croatian Ministry of science and technology, code 1–01–251, title „Representation theory“

**Scientific grants (as colaborator):**

- From December 11, 2015 the Croatian Scientific Center of Excelence for Quantum, and Complex Sistems and Repesentations of Lie Algebras (principal investigators Hrvoje Buljan and Pavle Pandžić)
- From June 1, 2014 a project of the Croatian Scientific Foundation „Dirac Operators in Representation Theory“ (principal investigator Pavle Pandžić)
- 2011–2012 and 2013–2014 Croatian–French bilateral scientific project Cogito (principal investigators Pavle Pandžić and Salah Mehdi)
- 2002–2007 a projekt of the Croatian Ministry of science and technology, code 0037106, title „Hilbert Modules and Operator Spaces“ (principal investigator Boris Guljaš)

**Awards and tributes:**

- March 2014. Honorary Doctorate from the University of Zadar
- from 1992 corresponding member of the Croatian Academy of Sciences and Arts
- 1987 honorary advisor of the University of Osijek
- 1984 Croatian anual award „Ruđer Bošković“ for scientific discovery
- 1973 award of the Balkan Mathematical Union for young scientists
- 1970 award „Seven SKOJ secretaries“ for young scientists
- 1965 rector’s award of the University of Zagreb

**Director of scientific conferences:**

- 2015 „Representation Theory XIV“, IUC, Dubrovnik
- 2013 „Representation Theory XIII“, IUC, Dubrovnik
- 2011 „Representation Theory XII“, IUC, Dubrovnik
- 2009 „Representation Theory XI“, IUC, Dubrovnik
- 2008 „Functional Analysis X“, IUC, Dubrovnik
- 2005 „Functional Analysis IX“, IUC, Dubrovnik
- 2004 „XI Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 2003 „Functional Analysis VIII“, IUC, Dubrovnik
- 2001 „Functional Analysis VII“, IUC, Dubrovnik
- 2001 „X Mathematikertreffen Zagreb–Graz“, Motovun
- 1999 „Functional Analysis VI“, IUC, Dubrovnik
- 1997 „Functional Analysis V“, IUC, Dubrovnik
- 1995 „IX Mathematikertreffen Zagreb–Graz“, Motovun
- 1993 „Functional Analysis IV“, IUC, Dubrovnik
- 1993 „VIII Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 1990 „VII Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 1989 „Functional Analysis III“, IUC, Dubrovnik
- 1988 „VI Mathematikertreffen Zagreb–Graz“, Opatija
- 1986 „V Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 1985 „Functional Analysis II“, IUC, Dubrovnik
- 1984 „IV Mathematikertreffen Zagreb–Graz“, Mali Lošinj
- 1982 „III Mathematikertreffen Zagreb–Graz“, Graz, Austria
- 1981 „Functional Analysis“, IUC, Dubrovnik
- 1980 „II Mathematikertreffen Zagreb–Graz“, Plitvice
- 1978 „Mathematikertreffen Zagreb–Graz“, Retzhoff, Austria

**Biography – other:**

Hrvoje Kraljević was born on March 16, 1944 in Zagreb. After Bachelor’s degree he initiated studying representation theory in Croatia. 1976–1990 editor and 1990–1995 editor–in–chief of the scientific journal “Glasnik matematički”. Member of the Croatian Mathematical Society, the American Mathematical Society and the European Mathematical Society. From 2007 the president of the Croatian Mathematical Society. Mentor of 6 PhD theses, 12 MSc theses and more than 100 Bachelor’s degree theses. Held 22 lectures in scientific conferences (mostly international) and 30 invited colloquium and seminar lectures in different scientific institutions. Held more than 30 different undergraduate courses in Zagreb, Osijek, Dubrovnik and Mostar, and 26 postgraduate courses at the departments of mathematics, physics and civil engineering in Zagreb. Published 29 scientific papers, two university textbooks, two secondary school textbooks and 15 Internet lecture notes. From January 2000 until July 2002. he was Minister of Science and Technology in the Government of the Republic of Croatia.

## Professor Mirko Primc

**Position:**

- Professor of Mathematic at the Faculty of Science University of Zagreb (Department of Mathematics)

**Fields of interest:**

- Representation theory of affine Lie algebras and vertex operator algebras

**Awards:**

- Croatian National Science Award for 1993 for natural sciences
- Award of the Croatian Academy of Sciences and Arts for 2000 for natural sciences

**Five selected publications: **

- J. Lepowsky and M. Primc, Structure of the standard modules for the affine Lie Algebra A1(1), Contemporary Math. 46, AMS, Providence, 1985, 1-84.
- M. Primc, Vertex operator construction of standard modules for An(1), Pacific J. Math. 162 (1994), 143–187.
- A. Meurman and M. Primc, Annihilating fields for standard modules of sl(2, C)~ and combinatorial identities, Memoirs Amer. Math. Soc. 652, AMS, 1999, 1-89.
- M. Primc, Basic representations for classical affine Lie algebras, J. Algebra 228 (2000), 1-50.
- M. Primc, Combinatorial bases of modules for affine Lie algebra B2(1), Cent. Eur. J. Math. 11 (2013), 197-225.

**PI on MZOS grant:**

- Infinite analysis (037002)
- Vertex operator algebras and infinite dimensional Lie algebras (037-0372794-2806)

**CV:**

Mirko Primc received a BSc degree in physics from the University of Zagreb in 1971 and defended his PhD thesis in mathematics at the same university in 1978. Since 1979 he is an assistant professor, since 1986 an associate professor and since 1993 a full professor at the University of Zagreb. Academic year 1980/81 he was a member at the Institute for Advanced Study in Princetonu, USA, academic year 1983/84 he was a member at the Mathematical Sciences Research Institute in Berkeley, USA, and in academic year 1991/92 he visited Department of Mathematics at the University of Lund, Sweden.

He mentored nine PhD theses and a number of BSc and MSc theses.

- Website: Link

## Ana Prlić

**Position:**

- Postdoctoral researcher at the Faculty of Science University of Zagreb (Department of Mathematics)

**Fields of interest:**

- Representations of semisimple Lie groups and algebras: Dirac operators in representation theory

**Awards:**

- Top scholarship for top students (2007)
- Dean’s award (2005 and 2006)

**Publications:**

- A. Prlić, Algebraic Dirac Induction for Nonholomorphic Discrete Series of SU(2,1), J. Lie Theory 26 (2016), no. 3, 889-910.
- A. Prlić, K-invariants in the algebra U(g) ⊗ C(p) for the group SU(2,1), Glas. Mat. 50 (2015), no. 2, 397-414

**Bio:**

Ana Prlić was born on November 6th, 1983 in Imotski. Under the mentorship of professor Hrvoje Kraljević she achieved a BSc in 2007 with the thesis title “Representations of the three-dimensional Lorentz group”. On May 27th, 2014 she obtained Ph.D. degree with the thesis “Algebraic Dirac induction for discrete series representations of the group SU(n,1)” under the mentorship of professors Hrvoje Kraljević and Pavle Pandžić.

From July 2008 tilI July 2014 she was employed as a teaching assistant at the Department of Mathematics, University of Zagreb. She has been employed as a postdoctoral researcher at the same faculty from July, 2014 till now.

AP authored two publications and gave a talk at four international conferences.