# Dr. Phillip Isaac

Phone: +61 7 3365 3267

Office: Priestley building (67), room 743 (level 7), UQ St Lucia campus

I am a senior lecturer in the School of Mathematics and Physics at The University of Queensland, Brisbane, Australia.

I received my PhD in mathematics from The University of Queensland in 2001. My PhD thesis was titled "Quasi Hopf superalgebras and their dual structures". My PhD supervisor was Prof. M.D. Gould.

For most of 2001 I worked at the Distributed Systems Technology Centre (DSTC) as a JAVA programmer/mathematician developing elliptic curve cryptographic software in the framework of the JAVA Security Architecture.

I lived in Tokyo for two years from late 2001 until 2003 while I did a postdoc at the Graduate School of Mathematical Sciences, The University of Tokyo.

Since 2004 I have been a lecturer in mathematics at UQ on various casual and fixed term positions. In September 2009 my position was made continuing.

In 2011 I received an Award for Teaching Excellence from the University of Queensland. This was one of five awarded across the university that year.

The last few years I have been a member of the Executive of the Australian and New Zealand Association of Mathematical Physics (ANZAMP) in the role of Secretary (2020-2021) and Chair (2022-2023). For 2022-2023 I was also a member of the Steering Committee and Council of the Australian Mathematical Society.

### Research

My research interests are concerned with the structure and representation theory of Lie algebras and superalgebras, related symmetry methods and applications to integrable quantum systems and other areas of mathematical physics.

### Publications

42. A.M.Almutairi, **P.S. Isaac**, *A connection between \( U_q(sl(3))\) and \(\mathbb{Z}_2\times \mathbb{Z}_2\)-graded special linear Lie colour algebras via Klein operators,* Journal of Mathematical Physics 65 (2024), 013503. [Link].

41. L. Bennett, A. Foerster, **P.S. Isaac**, J. Links, *Occupancy probabilities in superintegrable bosonic networks,
* Nuclear Physics B 998 (2024), 116406. [Link].

40. L. Bennett, **P.S. Isaac**, J. Links, *NOON state measurement probabilities and outcome fidelities: a Bethe ansatz approach,
* Journal of Physics A: Mathematical and Theoretical 56 (2023), 505202. [Link].

39. M.D. Gould, **P.S. Isaac**, J.L. Werry, *Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras,
* Journal of Physics A: Mathematical and Theoretical 55 (2022), 235201. [Link].

38. N. Aizawa, **P.S. Isaac**, J. Segar, *\(\mathbb{Z}_2\times \mathbb{Z}_2\) generalizations of
infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions,
* Reports on Mathematical Physics 85 (2020), 351. [Link]

37. Y. Shen, **P.S. Isaac**, J. Links, *Ground-state energy of a Richardson-Gaudin integrable BCS model,* SciPost Physics Core 2 (2020), 001. [Link]

36. **P.S. Isaac**, N.I. Stoilova, J. Van der Jeugt, *The \(\mathbb{Z}_2\times \mathbb{Z}_2\)-graded general linear Lie superalgebra,* Journal of Mathematical Physics 61 (2020), 011702. [Link]

35. M.D. Gould, **P.S. Isaac**, *Invariants and matrix elements of the quantum group \(U_q[gl(n,\mathbb{C})]\) revisited*, Journal of Physics A: Mathematical and Theoretical 52 (2019), 295201. [Link]

34. N. Aizawa, **P.S. Isaac**, J. Segar, *\(\mathbb{Z}_2\times \mathbb{Z}_2\) generalizations of \({\cal N} = 1\) superconformal Galilei algebras and their representations*, Journal of Mathematical Physics 60 (2019), 023507. [Link]

33. F. Alshammari, **P.S. Isaac**, I. Marquette, *On Casimir operators of conformal Galilei algebras*, Journal of Mathematical Physics 60 (2019), 013509. [Link]

32. Y. Shen, **P.S. Isaac**, J. Links, *Ground-state energies of the open and closed p+ip-pairing models from the Bethe Ansatz*, Nuclear Physics B 937 (2018), 28--55. [Link]

31. D. Agboola, **P.S. Isaac**, J. Links, *Energy-level crossings and number-parity effects in a bosonic tunneling model*, Journal of Physics B: Atomic, Molecular and Optical Physics 51 (2018), 145301. [Link]

30. F. Alshammari, **P.S. Isaac**, I. Marquette, *A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras*, Journal of Physics A: Mathematical and Theoretical 51 (2018), 065206. [Link]

29. J.L. Werry, **P.S. Isaac**, M.D. Gould, *Reduced Wigner coefficients for Lie superalgebra \(gl(m|n)\) corresponding to unitary representations and beyond*, Journal of Physics A: Mathematical and Theoretical 50 (2017), 365202. [Link]

28. D. Rubeni, J. Links, **P.S. Isaac**, A. Foerster, *Two-site Bose-Hubbard model with nonlinear tunneling: classical and quantum analysis*, Physical Review A 95 (2017), 043607. [Link]

27. **P.S. Isaac**, I. Marquette, *Families of 2D superintegrable anisotropic Dunkl oscillators and algebraic derivation of their spectrum*, Journal of Physics A: Mathematical and Theoretical 49 (2016), 115201. [Link]

26. I. Lukyanenko, **P.S. Isaac**, J. Links, *An integrable case of the p+ip pairing Hamiltonian interacting with its environment*, Journal of Physics A: Mathematical and Theoretical 49 (2016), 084001. [Link]

25. J.L. Werry, M.D. Gould, **P.S. Isaac**, *Matrix elements and duality for type 2 unitary representations of the Lie superalgebra \(gl(m|n)\)*, Journal of Mathematical Physics 56 (2015), 121703. [Link]

24. **P.S. Isaac**, J.L. Werry, M.D. Gould, *Characteristic identities for Lie (super)algebras*, Journal of Physics: Conference Series 597 (2015) 012045. [Link]

23. M.D. Gould, **P.S. Isaac**, *Reduced matrix elements of the orthosymplectic Lie superalgebra*, Journal of Physics A: Mathematical and Theoretical 48 (2015), 025201. [Link]

22. I. Lukyanenko, **P.S. Isaac**, J. Links, *On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system*, Nuclear Physics B 886 (2014), 364--398. [Link]

21. **P.S. Isaac**, I. Marquette, *On realizations of polynomial algebras with three generators via deformed oscillator algebras*, Journal of Physics A: Mathematical and Theoretical 47 (2014), 205203. [Link]

20. M.D. Gould, **P.S Isaac**, J.L. Werry, *Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra \(gl(m|n)\)*, Journal of Mathematical Physics 55 (2014), 011703. [Link]

19. A. Birrell, **P.S. Isaac**, J. Links, *Exactly solvable BCS-BEC crossover Hamiltonians*, in "Symmetries and Groups in Contemporary Physics'', Nankai Series in Pure, Applied Mathematics and Theoretical Physics 11 (2013), 161--166.
[Link]

18. M.D. Gould, **P.S. Isaac**, J.L. Werry, *Invariants and reduced matrix elements associated with the Lie superalgebra \(gl(m|n)\)*, Journal of Mathematical Physics 54 (2013), 013505. [Link]

17. N. Aizawa, **P.S. Isaac**, Y. Kimura, *Highest weight representations and Kac determinants for a class of conformal Galilei algebras with central extension*, International Journal of Mathematics 23 (2012), 1250118. [Link]

16. A. Birrell, **P.S. Isaac**, J.Links, *A variational approach for the Quantum Inverse Scattering Method*, Inverse Problems 28 (2012), 035008. [Link]

15. C. Dunning, **P.S. Isaac**, J. Links, S.-Z. Zhao, *BEC-BCS crossover in a
p+ip-wave pairing Hamiltonian coupled to bosonic molecular pairs*, Nuclear Physics B
848 (2011), 372--397. [Link]

14. P.E. Finch, K.A. Dancer, **P.S. Isaac**, J. Links, *Solutions of the Yang-Baxter
equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral
group algebras*, Nuclear Physics B 847 (2011), 387--412. [Link]

13. N. Aizawa, **P.S. Isaac**, * On irreducible representations of the exotic conformal Galilei algebra*,
Journal of Physics A: Mathematical and Theoretical 44 (2011), 035401. [Link]

12. C.W. Campbell, K.A. Dancer, **P.S. Isaac**, J. Links, * Bethe ansatz solution of an
integrable, non-Abelian anyon chain with \(D(D_3)\) symmetry*, Nuclear Physics
B 836 (2010), 171--185. [Link]

11. E.J. Tonkes, **P.S. Isaac**, V. Scharaschkin, * Assessment of an innovative system of
lecture notes in first year mathematics*, International
Journal of Mathematical Education in Science and Technology 40 (2009), 495--504. [Link]

10. K.A. Dancer, P.E. Finch, **P.S. Isaac**, J. Links, * Integrable
boundary conditions for a non-Abelian anyon chain with \(D(D_3)\) symmetry*, Nuclear
Physics B 812 (2009), 456--469. [Link]

9. S. Worsley, A. Bracken, K. Hibberd, **P.S. Isaac**, * Introducing a group
research project into a second-level mathematics course*, Proceedings of the National
UniServe Conference, The University of Sydney (2009), 125--131. [Link]

8. K.A. Dancer, P.E. Finch, **P.S. Isaac**, * Universal Baxterization for \(\mathbb{Z}\)-graded Hopf
algebras*, Journal of Physics A: Mathematical and Theoretical 40 (2007),
F1069--F1075. [Link]

7. **P.S. Isaac**, W.P. Joyce and J. Links, * An algebraic approach to
symmetric pre-monoidal statistics*, Journal of Algebra and Its Applications 6 (2007), 49--69. [Link]

6. K.A. Dancer, **P.S. Isac** and J. Links, * Representations of the
quantum doubles of finite group algebras and spectral parameter dependent
solutions of the Yang-Baxter equation*, Journal of Mathematical Physics 47 (2006),
103511. [Link]

5. L.D. Wagner, J. Links and **P.S. Isaac**, *Ribbon structure in symmetric
pre-monoidal categories*, Proceedings of the XXV International Colloquium on
Group Theoretical Methods in Physics, eds. G.S. Pogosyan, L.E. Vincent and K.B. Wolf, Institute of
Physics Conference Series 185 (2005), 557--562. [Link]

4. N. Aizawa, **P.S. Isaac**, *Weak Hopf algebras corresponding to \(U_q[sl_n]\)*,
Journal of Mathematical Physics 44, (2003), 5250--5267. [Link]

3. M.D. Gould, Y.-Z. Zhang, **P.S. Isaac**, *On quasi Hopf superalgebras*,
Communications in Mathematical Physics 224 (2001), 341--372. [Link]

2. M.D. Gould, Y.-Z. Zhang, **P.S. Isaac**, *Casimir invariants for
quasi-Hopf (super)algebras*, Journal of Mathematical Physics 41 (2000), 547--568. [Link]

1. M.D. Gould, **P.S. Isaac**, *Quasi-Lie algebras and a method for determining
non-degeneracy of the quasi-Lie product*, Group 22: Proceedings of the XXII International
Colloquium on Group Theoretical Methods in Physics, eds S.P. Corney, R. Delbourgo and P.D. Jarvis, International Press (1999), 418--422. [Link]