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Gröbner–Shirshov Bases for Irreducible sln + 1-Modules

✍ Scribed by Seok-Jin Kang; Kyu-Hwan Lee

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
169 KB
Volume
232
Category
Article
ISSN
0021-8693

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✦ Synopsis

We determine the Gröbner-Shirshov bases for finite-dimensional irreducible representations of the special linear Lie algebra sl n+1 and construct explicit monomial bases for these representations. We also show that each of these monomial bases is in 1-1 correspondence with the set of semistandard Young tableaux of a given shape.

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Gröbner Bases for the Rings of Special O
Gröbner Bases for the Rings of Special Orthogonal and 2 × 2 Matrix Invariants
✍ M Domokos; V Drensky 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 110 KB

We present a Gröbner basis for the ideal of relations among the standard generators of the algebra of invariants of the special orthogonal group acting on k-tuples of vectors. The cases of SO 3 and SO 4 are interpreted in terms of the algebras of invariants and semi-invariants of k-tuples of 2 × 2 m