Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup Q(n).
Kleshchev, Alexander.
Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup Q(n). - 1st ed. - 1 online resource (148 pages) - Memoirs of the American Mathematical Society ; v.220 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Abstract -- Introduction -- Set up -- Projective representations and Sergeev algebra -- Crystal graph approach -- Schur functor approach -- Modular branching rules -- Connecting the two approaches -- Some tensor products over ( ) -- Strategy of the proof and organization of the paper -- Chapter 1. Preliminaries -- 1.1. General Notation -- 1.2. The supergroup ( ) and its hyperalgebra -- 1.3. Highest weight theory -- Chapter 2. Lowering operators -- 2.1. Definitions -- 2.2. Properties of ^_ and ^_ -- 2.3. Supercommutator [ _^, _^( )] -- 2.4. Supercommutator [ ⱼ^, _^( )] -- 2.5. More on _^ _^( ) -- 2.6. Some coefficients -- Chapter 3. Some polynomials -- 3.1. Operators ^_ -- 3.2. Polynomials _^( ) -- 3.3. Polynomials ⁽¹⁾_( ) -- 3.4. Polynomials ⁽²⁾_( ) -- Chapter 4. Raising coefficients -- 4.1. Inductive formulas -- 4.2. The case of signed sets with only even elements -- 4.3. The case of signed sets with one odd element -- Chapter 5. Combinatorics of signature sequences -- 5.1. Marked signature sequences -- 5.2. Normal and good indices -- 5.3. Tensor conormal and tensor cogood indices -- 5.4. Removable and addable nodes for dominant -strict weights -- Chapter 6. Constructing ( -1)-primitive vectors -- 6.1. Construction: case [∏_ ᵦ( )_]=-^ -- 6.2. Construction: case [∏_ ᵦ( )_]=-^ and ᵢ, _ are not both divisible by -- 6.3. Construction: case ᵢ1\ and [∏_ _( )_]=+-^ -- 6.4. Extension: case _0\ , ᵢ1\ , [∏_ _( )_]=-^ -- 6.5. Extension: case ᵢ̸0\ , [∏_\ } ᵦ( )_]=-^, and _0\ , ᵢ1\ do not both hold -- 6.6. Extension: case _1\ , ᵢ0\ , and [∏_ _(\ )_]=+-^ -- Chapter 7. Main results on ( ) -- 7.1. Normal indices and primitive vectors -- 7.2. Criterion for existence of nonzero ( -1)-primitive vectors -- 7.3. The socle of the first level -- 7.4. Complement pairs -- 7.5. Primitive vectors in ( )⊗ * -- 7.6. Primitive vectors in ( )⊗ -- Chapter 8. Main results on projective representations of symmetric groups -- 8.1. Representations of Sergeev superalgebras -- 8.2. Proof of Theorem A -- 8.3. Proof of Theorem B -- 8.4. Projective representations of symmetric groups -- Bibliography.
9780821892053
Symmetry groups.
Modules (Algebra).
Operator theory.
Electronic books.
QA174.7.S96 -- .K54 2012eb
515/.724
Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup Q(n). - 1st ed. - 1 online resource (148 pages) - Memoirs of the American Mathematical Society ; v.220 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Abstract -- Introduction -- Set up -- Projective representations and Sergeev algebra -- Crystal graph approach -- Schur functor approach -- Modular branching rules -- Connecting the two approaches -- Some tensor products over ( ) -- Strategy of the proof and organization of the paper -- Chapter 1. Preliminaries -- 1.1. General Notation -- 1.2. The supergroup ( ) and its hyperalgebra -- 1.3. Highest weight theory -- Chapter 2. Lowering operators -- 2.1. Definitions -- 2.2. Properties of ^_ and ^_ -- 2.3. Supercommutator [ _^, _^( )] -- 2.4. Supercommutator [ ⱼ^, _^( )] -- 2.5. More on _^ _^( ) -- 2.6. Some coefficients -- Chapter 3. Some polynomials -- 3.1. Operators ^_ -- 3.2. Polynomials _^( ) -- 3.3. Polynomials ⁽¹⁾_( ) -- 3.4. Polynomials ⁽²⁾_( ) -- Chapter 4. Raising coefficients -- 4.1. Inductive formulas -- 4.2. The case of signed sets with only even elements -- 4.3. The case of signed sets with one odd element -- Chapter 5. Combinatorics of signature sequences -- 5.1. Marked signature sequences -- 5.2. Normal and good indices -- 5.3. Tensor conormal and tensor cogood indices -- 5.4. Removable and addable nodes for dominant -strict weights -- Chapter 6. Constructing ( -1)-primitive vectors -- 6.1. Construction: case [∏_ ᵦ( )_]=-^ -- 6.2. Construction: case [∏_ ᵦ( )_]=-^ and ᵢ, _ are not both divisible by -- 6.3. Construction: case ᵢ1\ and [∏_ _( )_]=+-^ -- 6.4. Extension: case _0\ , ᵢ1\ , [∏_ _( )_]=-^ -- 6.5. Extension: case ᵢ̸0\ , [∏_\ } ᵦ( )_]=-^, and _0\ , ᵢ1\ do not both hold -- 6.6. Extension: case _1\ , ᵢ0\ , and [∏_ _(\ )_]=+-^ -- Chapter 7. Main results on ( ) -- 7.1. Normal indices and primitive vectors -- 7.2. Criterion for existence of nonzero ( -1)-primitive vectors -- 7.3. The socle of the first level -- 7.4. Complement pairs -- 7.5. Primitive vectors in ( )⊗ * -- 7.6. Primitive vectors in ( )⊗ -- Chapter 8. Main results on projective representations of symmetric groups -- 8.1. Representations of Sergeev superalgebras -- 8.2. Proof of Theorem A -- 8.3. Proof of Theorem B -- 8.4. Projective representations of symmetric groups -- Bibliography.
9780821892053
Symmetry groups.
Modules (Algebra).
Operator theory.
Electronic books.
QA174.7.S96 -- .K54 2012eb
515/.724