Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Weyl module | Statement: [Verma module, relatedConcept, Weyl module]

Target entity: Weyl module
Context triple: [Verma module, relatedConcept, Weyl module]

• A. Verma module
  A Verma module is a type of highest-weight module over a Lie algebra that is freely generated from a highest-weight vector and plays a central role in the classification of representations of semisimple Lie algebras.
• B. Weyl character formula
  The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
• C. Weyl dimension formula
  The Weyl dimension formula is a fundamental result in representation theory that gives an explicit product expression for the dimension of each finite-dimensional irreducible representation of a semisimple Lie algebra or compact Lie group in terms of its highest weight and the root system.
• D. Weyl vector
  The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
• E. Weyl denominator
  The Weyl denominator is a key product expression in Lie theory that appears in the Weyl character formula, encoding the alternating sum over the Weyl group and playing a central role in describing characters of irreducible representations of semisimple Lie algebras.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Weyl module
Target entity description: A Weyl module is a finite-dimensional highest-weight representation of a semisimple Lie algebra (or algebraic group) that plays a central role in the classification and study of their representations.

• A. Verma module
  A Verma module is a type of highest-weight module over a Lie algebra that is freely generated from a highest-weight vector and plays a central role in the classification of representations of semisimple Lie algebras.
• B. Weyl character formula
  The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
• C. Weyl dimension formula
  The Weyl dimension formula is a fundamental result in representation theory that gives an explicit product expression for the dimension of each finite-dimensional irreducible representation of a semisimple Lie algebra or compact Lie group in terms of its highest weight and the root system.
• D. Weyl vector
  The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
• E. Weyl denominator
  The Weyl denominator is a key product expression in Lie theory that appears in the Weyl character formula, encoding the alternating sum over the Weyl group and playing a central role in describing characters of irreducible representations of semisimple Lie algebras.
• F. None of above. chosen