ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 30 Nov 2021 07:05:54 GMT2021-11-30T07:05:54Z50121- Invariants of S4 and the shape of sets of vectorshttps://scholarbank.nus.edu.sg/handle/10635/103446Title: Invariants of S4 and the shape of sets of vectors
Authors: Aslaksen, H.; Chan, S.-P.; Gulliksen, T.
Abstract: We study a representation of Sn that is related to the shape of sets of vectors in ℝn. We want to determine the invariants of this representation, and obtain a complete description for the case of S4.
Mon, 01 Jan 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034461996-01-01T00:00:00Z
- Determining summands in tensor products of Lie algebra representationshttps://scholarbank.nus.edu.sg/handle/10635/103126Title: Determining summands in tensor products of Lie algebra representations
Authors: Aslaksen, H.
Abstract: We give some results that enable us to find certain summands in tensor products of Lie algebra representations. We concentrate on the splitting of tensor squares into their symmetric and antisymmetric parts. Our results are valid for any Lie algebra of arbitrary rank, but we do not attempt to give the complete decomposition. © 1994.
Fri, 29 Apr 1994 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031261994-04-29T00:00:00Z
- K-theory for the integer Heisenberg groupshttps://scholarbank.nus.edu.sg/handle/10635/103467Title: K-theory for the integer Heisenberg groups
Authors: Aslaksen, H.; Lee, S.T.; Packer, J.
Abstract: We give a closed formula for topological K-theory of the homogeneous space N/Γ, where Γ is the standard integer lattice in the simply connected Heisenberg Lie group N of dimension 2n + 1, n ∈ ℤ+. The main tools in our calculations are obtained by computing diagonal forms for certain incidence matrices that arise naturally in combinatorics. © 1999 Kluwer Academic Publishers.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034671999-01-01T00:00:00Z
- Quaternionic determinantshttps://scholarbank.nus.edu.sg/handle/10635/104008Title: Quaternionic determinants
Authors: Aslaksen, H.
Mon, 01 Jan 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040081996-01-01T00:00:00Z
- Restricted homogeneous coordinates for the Cayley projective planehttps://scholarbank.nus.edu.sg/handle/10635/104054Title: Restricted homogeneous coordinates for the Cayley projective plane
Authors: Aslaksen, H.
Abstract: I. Porteous has shown that the Cayley projective plane can be coordinatized in a way resembling homogeneous coordinates. We will show how to construct line coordinates in a similar way. As an illustration, we give an explicit example to show that the Cayley projective plane is not Desarguean. © 1991 Kluwer Academic Publishers.
Fri, 01 Nov 1991 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040541991-11-01T00:00:00Z
- Generic 2×2 matrices with involutionhttps://scholarbank.nus.edu.sg/handle/10635/103338Title: Generic 2×2 matrices with involution
Authors: Aslaksen, H.; Tan, E.-C.
Abstract: Procesi has given a linear basis for the ring of m generic 2×2 matrices. We do the same for the ring of m generic 2×2 matrices with transpose involution. © 1994 Springer-Verlag.
Thu, 01 Dec 1994 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033381994-12-01T00:00:00Z
- Extending π-systems to bases of root systemshttps://scholarbank.nus.edu.sg/handle/10635/103255Title: Extending π-systems to bases of root systems
Authors: Aslaksen, H.; Lang, M.L.
Abstract: Let R be an indecomposable root system. It is well known that any root is part of a basis B of R. But when can you extend a set, C, of two or more roots to a basis B of R? A π-system is a linearly independent set of roots such that if α and β are in C, then α - β is not a root. We will use results of Dynkin and Bourbaki to show that with two exceptions, A3Bn and A7E8, an indecomposable π-system whose Dynkin diagram is a subdiagram of the Dynkin diagrams of R can always be extended to a basis of R. © 2005 Published by Elsevier Inc.
Sun, 15 May 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1032552005-05-15T00:00:00Z
- Defining relations of invariants of two 3 × 3 matriceshttps://scholarbank.nus.edu.sg/handle/10635/103110Title: Defining relations of invariants of two 3 × 3 matrices
Authors: Aslaksen, H.; Drensky, V.; Sadikova, L.
Abstract: Over a field of characteristic 0, the algebra of invariants of several n × n matrices under simultaneous conjugation by GLn is generated by traces of products of generic matrices. Teranishi, 1986, found a minimal system of eleven generators of the algebra of invariants of two 3 × 3 matrices. Nakamoto, 2002, obtained an explicit, but very complicated, defining relation for a similar system of generators over ℤ. In this paper we have found another natural set of eleven generators of this algebra of invariants over a field of characteristic 0 and have given the defining relation with respect to this set. Our defining relation is much simpler than that of Nakamoto. The proof is based on easy computer calculations with standard functions of Maple but the explicit form of the relation has been found with methods of representation theory of general linear groups. © 2006 Elsevier Inc. All rights reserved.
Sat, 01 Apr 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031102006-04-01T00:00:00Z
- Generators of matrix algebras in dimension 2 and 3https://scholarbank.nus.edu.sg/handle/10635/103337Title: Generators of matrix algebras in dimension 2 and 3
Authors: Aslaksen, H.; Sletsjøe, A.B.
Abstract: Let K be an algebraically closed field of characteristic zero and consider a set of 2 × 2 or 3 × 3 matrices. Using a theorem of Shemesh, we give conditions for when the matrices in the set generate the full matrix algebra. © 2008.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033372009-01-01T00:00:00Z
- Heavenly mathematics & cultural astronomy: A course at the National University of Singaporehttps://scholarbank.nus.edu.sg/handle/10635/104569Title: Heavenly mathematics & cultural astronomy: A course at the National University of Singapore
Authors: Aslaksen, H.
Abstract: I have introduced a general education course called Heavenly Mathematics and Cultural Astronomy [2] at the National University of Singapore. The goal of this course is to study astronomy in a cultural context with a tropical emphasis. Most astronomy books are written from a high northern latitude point of view, but Singapore is almost on the equator, so I aim to be "hemispherically-correct". Singapore is also a multi-racial society, where public holidays are determined using the Gregorian, Chinese, Islamic and Indian calendars. The course starts with an introduction to observational astronomy with an emphasis on the appearance of the Sun and the Moon from different parts of the world. I then give a fairly detailed description of the Gregorian, Chinese, Islamic and Indian calendars [1, 4, 5], and finish with a thorough discussion of the analemma, equation of time and navigation [3]. Being a mathematician, my approach is quite mathematical, but my emphasis is on geometrical reasoning. Formulas and computations may scare some students away, but they are surprisingly willing to struggle with complicated spatial visualization. © 2010 American Institute of Physics.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1045692010-01-01T00:00:00Z
- On Certain Rings of Highest Weight Vectorshttps://scholarbank.nus.edu.sg/handle/10635/103689Title: On Certain Rings of Highest Weight Vectors
Authors: Aslaksen, H.; Tan, E.C.; Zhu, C.B.
Abstract: Let Rm, n) be the ring of highest weight vectors of the action of Om × GLn on the polynomial algebra of m × n matrices. We determine Rm, 2 and find generators for Rm,3. In particular, the results about Rm,2 give branching rules and information about the structure of holomorphic representations of Sp4. © 1995 Academic Press. All rights reserved.
Mon, 01 May 1995 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1036891995-05-01T00:00:00Z
- Quivers and the Invariant Theory of Levi Subgroupshttps://scholarbank.nus.edu.sg/handle/10635/104012Title: Quivers and the Invariant Theory of Levi Subgroups
Authors: Aslaksen, H.; Tan, E.C.; Zhu, C.B.
Abstract: We develop a theory of invariants using the formalism of quivers, generalizing earlier results attributed to Procesi. As an application, let H be the Levi component of a parabolic subgroup of a classical Lie group G with Lie algebra g. We describe a finite set of generators for P[g]H, the space of H-invariant polynomials on g, as well as the H-invariants in the universal enveloping algebra, U(g)H, thus generalizing the results of Klink and Ton-That, and Zhu. © 1994 Academic Press. All rights reserved.
Tue, 15 Feb 1994 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040121994-02-15T00:00:00Z