overview

Prof Lee Soo Teck graduated with a BSc(Hons) degree from NUS in 1988, and joined NUS as a senior tutor in the same year. He was awarded the NUS Overseas Graduate Scholarship to pursue a PhD degree at Yale University. Upon graduation from Yale in 1993, he returned to the Department of Mathematics at NUS as a lecturer. His research interest is representation theory and classical invariant theory.

selected publications

##### Articles1

- (2014).
__Structure of holomorphic unitary representations: the case of đ_{2,2}__.*Automorphic Forms and Related Geometry*. 614, 139-170.

##### Academic Articles23

- (2020).
__Highest Weight Vectors in Plethysms__.*Communications in Mathematical Physics*. 378(3), 1817-1841. - (2020).
__Standard Bases for Tensor Products of Exterior Powers__.*Algebras and Representation Theory*. 23(3), 715-738. - (2018).
__Skew Pieri algebras of the general linear group__.*Journal of Mathematical Physics*. 59(12), 121702. - (2017).
__A reciprocity law and the skew Pieri rule for the symplectic group__.*Journal of Mathematical Physics*. 58(3), 031702. - (2017).
__Double Pieri algebras and iterated Pieri algebras for the classical groups__.*American Journal of Mathematics*. 139(2), 347-401. - (2013).
__Pieri algebras for the orthogonal and symplectic groups__.*Israel Journal of Mathematics*. 195(1), 215-245. - (2012).
__Why should the LittlewoodâRichardson Rule be true?__.*Bulletin of the American Mathematical Society*. 49(2), 187-236. - (2008).
__Degenerate principal series and local theta correspondence III: The case of complex groups__.*Journal of Algebra*. 319(1), 336-359. - (2008).
__Intersection of harmonics and Capelli identities for symmetric pairs__.*Journal of the Mathematical Society of Japan*. 60(4), 955-982. - (2007).
__Bases for some reciprocity algebras I__.*Transactions of the American Mathematical Society*. 359(09), 4359-4388. - (2007).
__Covariants of Spn(C) and degenerate principal series of GLn(H)__.*Journal of Functional Analysis*. 253(1), 18-42. - (2003).
__Degenerate principal series representations of Sp(p, q)__.*Israel Journal of Mathematics*. 137(1), 355-379. - (2001).
__On the (g,K)-cohomology of certain theta lifts__.*Pacific Journal of Mathematics*. 199(1), 93-110. - (1999).
__Degenerate Principal Series Representations of GLn(C) and GLn(R)__.*Journal of Functional Analysis*. 166(2), 244-309. - (1998).
__Degenerate principal series and local theta correspondence__.*Transactions of the American Mathematical Society*. 350(12), 5017-5046. - (1997).
__Degenerate principal series and local theta correspondence II__.*Israel Journal of Mathematics*. 100(1), 29-59. - (1994).
__On Some Degenerate Principal Series Representations of U(n,n)__.*Journal of Functional Analysis*. 126(2), 305-366.

##### Chapters1

- (2017).
__Standard Monomial Theory for Harmonics in Classical Invariant Theory__.*Representation Theory, Number Theory, and Invariant Theory*. (pp. 265-302).

research overview

My long term research program is to use the constructions and techniques of classical invariant theory to develop a new approach to solve a class of basic questions in representation theory. Let G be a complex classical group and H a subgroup of G of a certain type. Then a branching algebra R for (G,H) is an algebra whose structure encodes the branching rule from G to H. We have constructed branching algebras corresponding to certain classical symmetric pairs and also branching algebras associated with the iterated Pieri rules. We have also determined explicit bases for all these algebras, where the basis elements can be identified with highest weight vectors for H in a representation for G. Part of our results were used to give a new proof of the Littlewood-Richardson Rule which describes multiplicities in the tensor product of 2 irreducible representations of the general linear group. The branching algebras associated with the iterated Pieri rule were also used to determine the kernel of a map related to the structure of polynomial rings. Very recently, we were able to apply our techniques to describe all the highest weight vectors explicitly in plethysms in some cases.

teaching overview

A teacher's main role is to facilitate his students' learning of a subject and to ensure that every student's potential is stretched to the fullest. The following are the specific steps I take to promote learning: 1. Arouse my students' interest in the subject. 2. Explain basic concepts and principles clearly. 3. Provide suitable exercises or problems for my students to work on, and guide them, if necessary, to find solutions. 4. Emphasize correct learning attitudes. 5. Be approachable for consultation and willing to provide additional help.

recent teaching activities