𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Symplectic Groups, Symplectic Spreads, Codes, and Unimodular Lattices

✍ Scribed by Rudolf Scharlau; Pham Huu Tiep

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
485 KB
Volume
194
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

It is known that the symplectic group Sp p has two complex conjugate 2 n n Ε½ . Ε½ . irreducible representations of degree p q 1 r2 realized over ‫ޑ‬ y p , provided ' that p ' 3 mod 4. In the paper we give an explicit construction of an odd unimodu-Ε½ . Ε½ .

n n lar Sp p и 2-invariant lattice ⌬ p, n in dimension p q 1 for any p ' 3 mod 4.

2 n

Such a lattice has been constructed by R. Bacher and B. B. Venkov in the case p n s 27. A second main result says that these lattices are essentially unique. We Ε½ . Ε½ . show that for n G 3 the minimum of ⌬ p, n is at least p q 1 r2 and at most p Ε½ ny1.r2 . The interrelation between these lattices, symplectic spreads of ‫ކ‬ 2 n , and p self-dual codes over ‫ކ‬ is also investigated. In particular, using new results of U. p Dempwolff and L. Bader, W. M. Kantor, and G. Lunardon, we come to three extremal self-dual ternary codes of length 28.

πŸ“œ SIMILAR VOLUMES

Symplectic Groups and Permutation Polyno
Symplectic Groups and Permutation Polynomials, Part II
✍ Shreeram S. Abhyankar πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 198 KB

In the Preamble I shall give a running summary of Sections 1}11 without changing item numbers. For instance Result (3.2) and Remark (3.3) from Section 3 will be reproduced with the same designations. I shall write (P1), 2 , (P11) to indicate that I am summarizing Section 1, 2 , Section 11 of Part I,

Antiholomorphic Representations for Orth
Antiholomorphic Representations for Orthogonal and Symplectic Quantum Groups
✍ Pavel Ε Ε₯ovΔ±́ček πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 305 KB

The coadjoint orbits for the series B , C , and D are considered in the case when the base point is a multiple of a fundamental weight. A quantization of the big cell is suggested by means of introducing a )-algebra generated by holomorphic coordinate functions. Starting from this algebraic structu

Holomorphic Discrete Models of Semisimpl
Holomorphic Discrete Models of Semisimple Lie Groups and their Symplectic Constructions
✍ Meng-Kiat Chuah πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 257 KB

Let G be a connected real semisimple Lie group which contains a compact Cartan subgroup such that it has non-empty discrete series. A holomorphic discrete model of G is a unitary G-representation consisting of all its holomorphic discrete series with multiplicity one. We perform geometric quantizati

Some Characterizations of the Weil Repre
Some Characterizations of the Weil Representations of the Symplectic and Unitary Groups
✍ Pham Huu Tiep; Alexander E. Zalesskii πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 425 KB

Let G be a finite symplectic or unitary group. We characterize the Weil representations of G via their restriction to a standard subgroup. Then we complete the determination of complex representations of G with specific minimal polynomials of certain elements by showing that they coincide with the W

A Probabilistic Approach to Conjugacy Cl
A Probabilistic Approach to Conjugacy Classes in the Finite Symplectic and Orthogonal Groups
✍ Jason Fulman πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 135 KB

Markov chains are used to give a purely probabilistic way of understanding the conjugacy classes of the finite symplectic and orthogonal groups in odd characteristic. As a corollary of these methods, one obtains a probabilistic proof of Steinberg's count of unipotent matrices and generalizations of