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Updated: Aug 9, 2026
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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Standard basis in supersymplectic algebras
1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139.
Summary
This study provides an integral standard basis for products of Pfaffians with mixed-sign variables. These findings advance invariant theory applications.
Area of Science:
- Algebraic Geometry
- Commutative Algebra
- Invariant Theory
Background:
- Pfaffians are important in algebraic geometry and representation theory.
- Standard bases are crucial for computations in polynomial rings.
- Understanding products of Pfaffians is key to advancing invariant theory.
Purpose of the Study:
- To introduce an integral standard basis for products of Pfaffians.
- To handle both positively and negatively signed variables within Pfaffian products.
- To explore the implications of this new basis for invariant theory.
Main Methods:
- Development of an integral standard basis tailored for Pfaffian products.
- Utilizing techniques from computational algebra and algebraic geometry.
- Derivation of applications within the framework of invariant theory.
Main Results:
- An explicit integral standard basis is established for products of Pfaffians.
- The basis effectively manages variables with differing signs.
- New applications in invariant theory are demonstrated.
Conclusions:
- The integral standard basis offers a powerful computational tool.
- This work bridges Pfaffian analysis with invariant theory.
- Further research can explore more complex Pfaffian structures.
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