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It's older than 20 years but otherwise the paper where Kashiwara and Vergne introduced their conjecture definitely qualify https://link.springer.com/article/10.1007/BF01579213

There is an important theorem of Duflo stating that the PBW isomorphism for a finite dimensional Lie algebra (in characteristic 0) can be twisted so that its restriction to the invariant part actually become an algebra isomorphism $U(\mathfrak g)^{\mathfrak g}\cong S(\mathfrak g)^{\mathfrak g}$.

The original proof is complicated and require a lot of case by case study. Kashiwara and Vergne suggest a very natural uniform proof of that result. Roughly speaking they postulate that the pull-back of the product on $U(\mathfrak g)$ to $S(\mathfrak g)$ through this twisted version of the PBW isomorphism can be written as $m\circ F$ where $m$ is the multiplication of $S(\mathfrak g)$ and $F$ is an automorphism of a very special form. Then they "rescale" it by introducting a parameter $t$, and observe that Duflo's theorem would follow from the existence of such an $F$ satisfying a certain differential equation w.r.t the parameter $t$. They also observe this would in fact imply a stronger statement, giving an isomorphism between invariant distribution on $\mathfrak g$ and its group $G$ with small suport. Their conjecture is thus really important in harmonic analysis and representation theory.

The main result of their paper is a proof of that conjecture in the solvable case, which can be done in a fairly elementary way. After that, several special cases were proven, but a general proof was given only in 2005 (by Alekseev--Meinrenken) and uses some high level machinery related to Kontsevich's proof of his deformation quantization theorem. Since then this new theorem has been connected to a surprisingly wide range of topics, including Grothenideck-Teichmueller theory, Etingof--Kazhdan theorem, quantum topology and the study of the Atiyah--Bott--Goldman Poisson structure on moduli spaces of flat connections.

It's older than 20 years but otherwise the paper where Kashiwara and Vergne introduced their conjecture definitely qualify https://link.springer.com/article/10.1007/BF01579213

There is an important theorem of Duflo stating that the PBW isomorphism for a finite dimensional Lie algebra (in characteristic 0) can be twisted so that its restriction to the invariant part actually become an algebra isomorphism $U(\mathfrak g)^{\mathfrak g}\cong S(\mathfrak g)^{\mathfrak g}$.

The original proof is complicated and require a lot of case by case study. Kashiwara and Vergne suggest a very natural uniform proof of that result. Roughly speaking they postulate that the pull-back of the product on $U(\mathfrak g)$ to $S(\mathfrak g)$ through this twisted version of the PBW isomorphism can be written as $m\circ F$ where $m$ is the multiplication of $S(\mathfrak g)$ and $F$ is an automorphism of a very special form. Then they "rescale" it by introducting a parameter $t$, and observe that Duflo's theorem would follow from the existence of such an $F$ satisfying a certain differential equation w.r.t the parameter $t$. They also observe this would in fact imply a stronger statement, giving an isomorphism between invariant distribution on $\mathfrak g$ and its group $G$ with small suport. Their conjecture is thus really important in harmonic analysis and representation theory.

The main result of their paper is a proof of that conjecture in the solvable case, which can be done in a fairly elementary way. After that, several special cases were proven, but a general proof was given only in 2005 (by Alekseev--Meinrenken) and uses some high level machinery related to Kontsevich's proof of his deformation quantization theorem. Since then this now theorem has been connected to a surprisingly wide range of topics, including Grothenideck-Teichmueller theory, Etingof--Kazhdan theorem, quantum topology and the study of the Atiyah--Bott--Goldman Poisson structure on moduli spaces of flat connections.

It's older than 20 years but otherwise the paper where Kashiwara and Vergne introduced their conjecture definitely qualify https://link.springer.com/article/10.1007/BF01579213

There is an important theorem of Duflo stating that the PBW isomorphism for a finite dimensional Lie algebra (in characteristic 0) can be twisted so that its restriction to the invariant part actually become an algebra isomorphism $U(\mathfrak g)^{\mathfrak g}\cong S(\mathfrak g)^{\mathfrak g}$.

The original proof is complicated and require a lot of case by case study. Kashiwara and Vergne suggest a very natural uniform proof of that result. Roughly speaking they postulate that the pull-back of the product on $U(\mathfrak g)$ to $S(\mathfrak g)$ through this twisted version of the PBW isomorphism can be written as $m\circ F$ where $m$ is the multiplication of $S(\mathfrak g)$ and $F$ is an automorphism of a very special form. Then they "rescale" it by introducting a parameter $t$, and observe that Duflo's theorem would follow from the existence of such an $F$ satisfying a certain differential equation w.r.t the parameter $t$. They also observe this would in fact imply a stronger statement, giving an isomorphism between invariant distribution on $\mathfrak g$ and its group $G$ with small suport. Their conjecture is thus really important in harmonic analysis and representation theory.

The main result of their paper is a proof of that conjecture in the solvable case, which can be done in a fairly elementary way. After that, several special cases were proven, but a general proof was given only in 2005 (by Alekseev--Meinrenken) and uses some high level machinery related to Kontsevich's proof of his deformation quantization theorem. Since then this now theorem has been connected to a surprisingly wide range of topics, including Grothenideck-Teichmueller theory, Etingof--Kazhdan theorem, quantum topology and the study of the Atiyah--Bott--Goldman Poisson structure on moduli spaces of flat connections.

It's older than 20 years but otherwise the paper where Kashiwara and Vergne introduced their conjecture definitely qualify https://link.springer.com/article/10.1007/BF01579213

There is an important theorem of Duflo stating that the PBW isomorphism for a finite dimensional Lie algebra (in characteristic 0) can be twisted so that its restriction to the invariant part actually become an algebra isomorphism $U(\mathfrak g)^{\mathfrak g}\cong S(\mathfrak g)^{\mathfrak g}$.

The original proof is complicated and require a lot of case by case study. Kashiwara and Vergne suggest a very natural uniform proof of that result. Roughly speaking they postulate that the pull-back of the product on $U(\mathfrak g)$ to $S(\mathfrak g)$ through this twisted version of the PBW isomorphism can be written as $m\circ F$ where $m$ is the multiplication of $S(\mathfrak g)$ and $F$ is an automorphism of a very special form. Then they "rescale" it by introducting a parameter $t$, and observe that Duflo's theorem would follow from the existence of such an $F$ satisfying a certain differential equation w.r.t the parameter $t$. They also observe this would in fact imply a stronger statement, giving an isomorphism between invariant distribution on $\mathfrak g$ and its group $G$ with small suport. Their conjecture is thus really important in harmonic analysis and representation theory.

The main result of their paper is a proof of that conjecture in the solvable case, which can be done in a fairly elementary way. After that, several special cases were proven, but a general proof was given only in 2005 (by Alekseev--Meinrenken) and uses some high level machinery related to Kontsevich's proof of his deformation quantization theorem. Since then this new theorem has been connected to a surprisingly wide range of topics, including Grothenideck-Teichmueller theory, Etingof--Kazhdan theorem, quantum topology and the study of the Atiyah--Bott--Goldman Poisson structure on moduli spaces of flat connections.

It's older than 20 years but otherwise the paper where Kashiwara and Vergne introduced their conjecture definitely qualify https://link.springer.com/article/10.1007/BF01579213

There is an important theorem of Duflo stating that the PBW isomorphism for a finite dimensional Lie algebra (in characteristic 0) can be twisted so that its restriction to the invariant part actually become an algebra isomorphism $U(\mathfrak g)^{\mathfrak g}\cong S(\mathfrak g)^{\mathfrak g}$.

The original proof is complicated and require a lot of case by case study. Kashiwara and Vergne suggest a very natural uniform proof of that result. Roughly speaking they postulate that the pull-back of the product on $U(\mathfrak g)$ to $S(\mathfrak g)$ through this twisted version of the PBW isomorphism can be written as $m\circ F$ where $m$ is the multiplication of $S(\mathfrak g)$ and $F$ is an automorphism of a very special form. Then they "rescale" it by introducting a parameter $t$, and observe that Duflo's theorem would follow from the existence of such an $F$ satisfying a certain differential equation w.r.t the parameter $t$. They also observe this would in fact imply a stronger statement, giving an isomorphism between invariant distribution on $\mathfrak g$ and its group $G$ with small suport. Their conjecture is thus really important in harmonic analysis and representation theory.

The main result of their paper is a proof of that conjecture in the solvable case, which can be done in a fairly elementary way. After that, several special cases were proven, but a general proof was given only in 2005 and uses some high level machinery related to Kontsevich's proof of his deformation quantization theorem. Since then this now theorem has been connected to a surprisingly wide range of topics, including Grothenideck-Teichmueller theory, Etingof--Kazhdan theorem, quantum topology and the study of the Atiyah--Bott--Goldman Poisson structure on moduli spaces of flat connections.

It's older than 20 years but otherwise the paper where Kashiwara and Vergne introduced their conjecture definitely qualify https://link.springer.com/article/10.1007/BF01579213

There is an important theorem of Duflo stating that the PBW isomorphism for a finite dimensional Lie algebra (in characteristic 0) can be twisted so that its restriction to the invariant part actually become an algebra isomorphism $U(\mathfrak g)^{\mathfrak g}\cong S(\mathfrak g)^{\mathfrak g}$.

The original proof is complicated and require a lot of case by case study. Kashiwara and Vergne suggest a very natural uniform proof of that result. Roughly speaking they postulate that the pull-back of the product on $U(\mathfrak g)$ to $S(\mathfrak g)$ through this twisted version of the PBW isomorphism can be written as $m\circ F$ where $m$ is the multiplication of $S(\mathfrak g)$ and $F$ is an automorphism of a very special form. Then they "rescale" it by introducting a parameter $t$, and observe that Duflo's theorem would follow from the existence of such an $F$ satisfying a certain differential equation w.r.t the parameter $t$. They also observe this would in fact imply a stronger statement, giving an isomorphism between invariant distribution on $\mathfrak g$ and its group $G$ with small suport. Their conjecture is thus really important in harmonic analysis and representation theory.

The main result of their paper is a proof of that conjecture in the solvable case, which can be done in a fairly elementary way. After that, several special cases were proven, but a general proof was given only in 2005 (by Alekseev--Meinrenken) and uses some high level machinery related to Kontsevich's proof of his deformation quantization theorem. Since then this now theorem has been connected to a surprisingly wide range of topics, including Grothenideck-Teichmueller theory, Etingof--Kazhdan theorem, quantum topology and the study of the Atiyah--Bott--Goldman Poisson structure on moduli spaces of flat connections.