Struct KashiwaraCrystal 

pub struct KashiwaraCrystal { /* private fields */ }

A finite type-A Kashiwara crystal represented by its colored graph.

Vertices are stable VertexId values 0..vertex_count. A zero-based index i selects the partial raising and lowering operators e_i and f_i. Weights are stored in fundamental-weight coordinates. The complete Cartan matrix is defining context, so equal-rank but mathematically different crystal families cannot be combined accidentally.

Implementations

impl KashiwaraCrystal

pub fn type_a_letters(rank: usize) -> Result<Self, CombinError>

Construct the standard letter crystal B(Lambda_1) of type A_rank.

pub fn type_a_tableaux( rank: usize, shape: &Partition, ) -> Result<Self, CombinError>

Construct the semistandard-tableau crystal B(shape) of type A_rank.

The alphabet is 1..=rank+1, rows are weakly increasing, and columns are strictly increasing. The shape and exact representation-size bounds are checked before the tableaux are materialized.

pub fn rank(&self) -> usize

Cartan rank, equal to the number of Kashiwara colors.

pub fn vertex_count(&self) -> usize

Number of vertices in the explicit colored graph.

pub fn cartan_matrix(&self) -> &[Vec<i64>]

Defining Cartan matrix for the crystal context.

pub fn weight(&self, vertex: VertexId) -> Result<&[i64], CombinError>

Weight of a vertex in fundamental-weight coordinates.

pub fn e( &self, index: usize, vertex: VertexId, ) -> Result<Option<VertexId>, CombinError>

Apply the Kashiwara raising operator e_index.

pub fn f( &self, index: usize, vertex: VertexId, ) -> Result<Option<VertexId>, CombinError>

Apply the Kashiwara lowering operator f_index.

pub fn epsilon_phi( &self, index: usize, vertex: VertexId, ) -> Result<(usize, usize), CombinError>

Return (epsilon_index(vertex), phi_index(vertex)), the upward and downward distances along one colored string.

pub fn highest_weight_vertices(&self) -> Vec<VertexId>

Vertices killed by every raising operator.

pub fn character(&self) -> BTreeMap<Vec<i64>, u64>

Weight-multiplicity character in deterministic weight order.

pub fn tensor(&self, rhs: &Self) -> Result<Self, CombinError>

Form the right-to-left Kashiwara tensor product.

Vertex (left, right) has identifier left * rhs.vertex_count() + right. The Cartan matrices must agree exactly, and the complete allocation is checked before materialization.

Trait Implementations

impl Clone for KashiwaraCrystal

fn clone(&self) -> KashiwaraCrystal

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for KashiwaraCrystal

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for KashiwaraCrystal

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for KashiwaraCrystal

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl PartialEq for KashiwaraCrystal

fn eq(&self, other: &KashiwaraCrystal) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl SemanticType for KashiwaraCrystal

const TYPE_ID: &'static str = "noether/combin/KashiwaraCrystal@1"

Versioned, language-neutral semantic identity.

fn canonical_bytes(&self) -> Result<Vec<u8>, NoetherError>

Serialize without backend- or language-specific identity.

fn describe() -> &'static TypeDescription

Return static discovery metadata for the type.

impl Serialize for KashiwaraCrystal

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl Eq for KashiwaraCrystal

impl StructuralPartialEq for KashiwaraCrystal