How Much Do You Know About Alvis-curtis Duality?

1) What's an idempotent?

It denotes an element of a set that is unchanged in value when multiplied or otherwise operated on by itself.

It denotes several elements of a set that is unchanged in value when multiplied or otherwise operated on by itself.

It denotes 10 elements of a curve that is unchanged in value when added or otherwise operated on by itself.

An idempotent is an element of a set that remains unchanged in value when multiplied or operated on by itself. This means that if you multiply or perform any operation on the element with itself, the result will be the same element.

Explanation

An idempotent is an element of a set that remains unchanged in value when multiplied or operated on by itself. This means that if you multiply or perform any operation on the element with itself, the result will be the same element.

2) Who invented the Alvis Curtis duality?

Charles W.Curtis

Dean Alvis

Kawanaka

Carter

Charles W. Curtis is credited with inventing the Alvis Curtis duality.

Explanation

Charles W. Curtis is credited with inventing the Alvis Curtis duality.

3) What's a parabolic induction?

It's a method of constructing representation of a reductive group from representation of its common subgroups.

It's a method of constructing representation of a inclusive group from representation of its parabolic subgroups.

It's a method of constructing representation of a reductive group from representation of its parabolic subgroups.

It's a method of constructing representation of a reductive group from representation of its subgroups.

A parabolic induction is a method of constructing a representation of a reductive group from the representation of its parabolic subgroups. This means that by studying the representations of the parabolic subgroups, we can build a representation of the larger reductive group.

Explanation

A parabolic induction is a method of constructing a representation of a reductive group from the representation of its parabolic subgroups. This means that by studying the representations of the parabolic subgroups, we can build a representation of the larger reductive group.

4) What's the other term for Steinberg representation?

Steinberg plan

Steinberg module

Steinberg multiplication

Steinberg addition

The other term for Steinberg representation is Steinberg module.

Explanation

The other term for Steinberg representation is Steinberg module.

5) What's the other term for cuspidal representation?

Cuspidal identity

Cuspidal formula

Cuspidal division

Cuspidal character

The other term for cuspidal representation is cuspidal character. A cuspidal character is a representation of a group that is trivial on all its proper parabolic subgroups. It is a character that cannot be induced from a character of a proper parabolic subgroup.

Explanation

The other term for cuspidal representation is cuspidal character. A cuspidal character is a representation of a group that is trivial on all its proper parabolic subgroups. It is a character that cannot be induced from a character of a proper parabolic subgroup.

6) What's the Gelfand-Graev representation?

It's a representation of a reductive group over a infinite field.

It's a representation of a inclusive group over a finite field.

It's a representation of a reductive group over a finite field.

It's a representation of a reductive group over a great field.

The Gelfand-Graev representation is a representation of a reductive group over a finite field. This means that it is a way of expressing the elements of a reductive group (a type of algebraic group) using matrices or linear transformations, where the elements are defined over a finite field. This representation is important in the study of algebraic groups and has applications in various areas of mathematics and theoretical physics.

Explanation

The Gelfand-Graev representation is a representation of a reductive group over a finite field. This means that it is a way of expressing the elements of a reductive group (a type of algebraic group) using matrices or linear transformations, where the elements are defined over a finite field. This representation is important in the study of algebraic groups and has applications in various areas of mathematics and theoretical physics.

7) What is the Alvis Curtis Duality?

It is an isometry on generalized addition

It is an isometry on generalized multiplication

It is an isometry on generalized functions

It is an isometry on generalized characters

The Alvis Curtis Duality refers to an isometry on generalized characters. This means that it preserves the distance between two generalized characters, which are mathematical objects that represent certain properties or features of a system. The Alvis Curtis Duality ensures that the relationship between these generalized characters remains consistent and unchanged, regardless of any transformations or operations applied to them.

Explanation

The Alvis Curtis Duality refers to an isometry on generalized characters. This means that it preserves the distance between two generalized characters, which are mathematical objects that represent certain properties or features of a system. The Alvis Curtis Duality ensures that the relationship between these generalized characters remains consistent and unchanged, regardless of any transformations or operations applied to them.

8) What's duality?

It's a group of mathematical structures into other concepts.

It's a group of theorems into other concepts.

It's a group of operations into other concepts.

It's a group of concepts, theorems/mathematical structures into other concepts.

Duality refers to a group of concepts, theorems, and mathematical structures that can be transformed or related to other concepts. This suggests that duality involves a connection or correspondence between different mathematical ideas, allowing for a deeper understanding and analysis of the subject matter.

Explanation

Duality refers to a group of concepts, theorems, and mathematical structures that can be transformed or related to other concepts. This suggests that duality involves a connection or correspondence between different mathematical ideas, allowing for a deeper understanding and analysis of the subject matter.

9) In what years was this theory invented?

1979

1980

1950

1880

The theory was invented in 1980.

Explanation

The theory was invented in 1980.

10) What is a (B, N) pair?

It is a structure or groups of Lie type that allows 2 to give uniform proofs of many results.

It is a structure or groups of Lie type that allows 3 to give uniform proofs of many results.

It is a structure or groups of Lie type that allows 4 to give uniform proofs of many results.

It is a structure or groups of Lie type that allows 1 to give uniform proofs of many results.

A (B, N) pair refers to a structure or groups of Lie type that allows 1 to give uniform proofs of many results. This means that by utilizing this structure or group, one can provide consistent and generalized proofs for a wide range of outcomes or conclusions.

Explanation

A (B, N) pair refers to a structure or groups of Lie type that allows 1 to give uniform proofs of many results. This means that by utilizing this structure or group, one can provide consistent and generalized proofs for a wide range of outcomes or conclusions.