Skip to main content
MathOverflow

Return to Question

deleted 1 character in body; edited title
Source Link
Allen Knutson
Allen Knutson
  • 27.9k
  • 4
  • 54
  • 152

Dimension of the zero weight space in $V_{2\rho}$

Let $\rho$ be the half sum of the positive roots (also the sum of fundmental weights) for $SL_n(\mathbb C)$. Then $2ρ$ is in the root lattice. Then what is the dimension of the zero weight space for the irreducible representation $V_{2\rho}$  ? What do the weights look like in this case ?

Dimension of the zero weight space

Let $\rho$ be the half sum of the positive roots (also the sum of fundmental weights) for $SL_n(\mathbb C)$. Then $2ρ$ is in the root lattice. Then what is the dimension of the zero weight space for the irreducible representation $V_{2\rho}$  ? What do the weights look like in this case ?

Dimension of the zero weight space in $V_{2\rho}$

Let $\rho$ be the half sum of the positive roots (also the sum of fundmental weights) for $SL_n(\mathbb C)$. Then $2ρ$ is in the root lattice. Then what is the dimension of the zero weight space for the irreducible representation $V_{2\rho}$? What do the weights look like in this case ?

added 1 character in body
Source Link
Allen Knutson
Allen Knutson
  • 27.9k
  • 4
  • 54
  • 152

Let $\rho$ be the half sum of the positive roots (also the sum of fundmental weights) for $SL_n(\mathbb C)$. Then $2ρ$ is in the root lattice. Then what is the dimension of the zero weight space for the irreducible representation $V_{2\rho}$ ? HowWhat do the weights look like in this case ?

Let $\rho$ be the half sum of the positive roots (also the sum of fundmental weights) for $SL_n(\mathbb C)$. Then $2ρ$ is in the root lattice. Then what is the dimension of the zero weight space for the irreducible representation $V_{2\rho}$ ? How do the weights look like in this case ?

Let $\rho$ be the half sum of the positive roots (also the sum of fundmental weights) for $SL_n(\mathbb C)$. Then $2ρ$ is in the root lattice. Then what is the dimension of the zero weight space for the irreducible representation $V_{2\rho}$ ? What do the weights look like in this case ?

Source Link
Jack
Jack
  • 31
  • 1

Dimension of the zero weight space

Let $\rho$ be the half sum of the positive roots (also the sum of fundmental weights) for $SL_n(\mathbb C)$. Then $2ρ$ is in the root lattice. Then what is the dimension of the zero weight space for the irreducible representation $V_{2\rho}$ ? How do the weights look like in this case ?